Given a Utility function, U(x,y), why is multiplying U(x,y) * x not a monotonic transformation?

Question: If $x$, is a commodity and it is s.t. $x \geq 0$ (it is always nonnegative) how will multiplying it times a utility function $U(x,y)$ NOT yield a simple monotonic transformation?
Answer: Because $x$ is not a constant, and therefore multiplying $U(x,y)$ by $x$ does not necessarily preserve the ordering between bundles.
For instance, consider the function $U(x,y)=x+y$, and the bundles $(x_0,y_0)=(2,0)$ and $(x_1,y_1)=(1,2)$. We have
\begin{equation*}
U(x_0,y_0)=2 < U(x_1,y_1)=3
\end{equation*}
but
\begin{equation*}
x_0 U(x_0,y_0) = 4 > x_1 U(x_1,y_1) = 3
\end{equation*}
Hence multiplying $U$ by $x$ changes the preferences, therefore is not a monotonic transformation.
As a side note, multiplying the utility function by a constant provides a monotonic transformation if the constant is positive, and not only nonnegative as you assumed (if the constant is zero the orderings are obviously not preserved).
Comment: Perfect explanation yet simple to understand. That's what we need.
Answer: The utility function $U'$ is a monotonic transformation  of $U$ if there is a strictly monotonically increasing function $f$ for which
$$
\forall x,y: \ f(U(x,y)) = U'(x,y)
$$
Larger values of $U(x,y)$ should always get larger values assigned. But with the function you outlined this is not the case if $U(x_1,y_1) \leq U(x_2,y_2)$ and
$$
\frac{U(x_2,y_2)}{U(x_1,y_1)} \leq \frac{x_1}{x_2}.
$$
Basically the order between bundles $(x_1,y_1)$ and $(x_2,y_2)$ may change depending on the ratio of their original utilities and the ratio of $x_1$ and $x_2$. An example has been provided by @Oliv.
Answer: Take any utility function $f(x)$. Just because $x\geq0$ doesn't mean $f(x)>0$. There are plenty (infinitely many) of utility functions that are sometime negative and sometimes positive.
Consider one $U = x-5$ This is person has exactly the same preference ordering as someone with preferences $U = x-10$, $U = x$, and $U = x+5$. Now imagine multiplying these utility functions by x. This makes the negative utility values positive at different values of x. We can tell that because the utility functions have the same ordering of the utility values of x.

Now consider the those same functions transformed by multiplying by x.

We can see that these transformed functions now actually prefer very low values of x to very high ones.


How best to grow my small amount of money starting at a young age?

Question: As someone close to being an adult and going to college, I have earned a small amount of money ($3000) and am looking to start my lifetime savings and get a head start by investing my money rather that simply holding it in a savings account.  Assuming that I can invest it any way I please, how can I best go about growing my money so I have a sizable amount by the time I graduate from college and need a house or car?  I currently have it invested in sector mutual funds but with the rise and fall of the stock market, is this really the best way to prepare long-term?
Comment: This is not a duplicate, since this OP is *starting* college, and the linked question already graduated.
Comment: Put that straight into a Roth IRA, and invest it *for growth*.  If you don't know how to invest for growth, stop by your university's donor relations office and ask them how they invest their Endowment.  Because an IRA is an endowment for you, and at age 20 your investment goals are exactly the same.  Investing in an IRA at such a young age will have an explosive effect on its growth, $3k is likely to balloon to $100k by retirement just all by itself.  Good retirement!  Get an IRA at a discount brokerage (e.g. Fidelity) and slap it in index ETFs which have the lowest possible expense ratios.
Answer: (Congrats on earning/saving $3K and not wanting to blow it all on immediate gratification!)

I currently have it invested in sector mutual funds but with the rise and fall of the stock market, is this really the best way to prepare long-term?

Long-term?  Yes!
However... four years is not long term.  It is, in fact, borderline short term.  (When I was your age, that was incomprehensible too, but trust me: it's true.)
The problem is that there's an inverse relationship between reward and risk: the higher the possible reward, the greater the risk that you'll lose a big chunk of it.
I invest that middle-term money in a mix of junk high yield bond funds and "high" yield savings accounts at an online bank.  My preferences are HYG purchased at Fidelity (EDIT: because it's commission-free and I buy a few hundred dollars worth every month), and Ally Bank.
Answer: I would like to add my accolades in saving $3000, it is an accomplishment that the majority of US households are unable to achieve. source
While it is something, in some ways it is hardly anything.  Working part time at a entry level job will earn you almost three times this amount per year, and with the same job you can earn about as much in two weeks as this investment is likely to earn, in the market in one year.
All this leads to one thing:  At your age you should be looking to increase your income.  No matter if it is college or a high paying trade, whatever you can do to increase your life time earning potential would be the best investment for this money.
I would advocate a more patient approach.  Stick the money in the bank until you complete your education enough for an "adult job".  Use it, if needed, for training to get that adult job.  Get a car, a place of your own, and a sufficient enough wardrobe.  Save an emergency fund.  Then invest with impunity.
Imagine two versions of yourself.  One with basic education, a average to below average salary, that uses this money to invest in the stock market.  Eventually that money will be needed and it will probably be pulled out of the market at an in opportune time.  It might worth less than the original 3K!
Now imagine a second version of yourself that has an above average salary due to some good education or training.  Perhaps that 3K was used to help provide that education.  However, this second version will probably earn 25,000 to 75,000 per year then the first version.  Which one do you want to be?  Which one do you think will be wealthier?
Better educated people not only earn more, they are out of work less.  You may want to look at this chart.
Comment: @RonJohn how is he paying for that college?  Could those plans go awry?  Best to keep in savings for now.
Comment: @Peter he specifically states in the first sentence that he's going to college, so half -- or more -- of your answer answers the wrong question.
Comment: "*how is he paying for that college?*"  That's irrelevant to the question. "*Best to keep in savings for now.*"  That was my answer, too.
Comment: @RonJohn How the OP is paying for college is not irrelevant. If the OP is keeping 3k in a savings account evening 0.1% interest while taking out student loans at 5%, then it's worth considering using the 3k for college expenses if the OP otherwise has enough of an emergency fund.
Comment: @Eric (1) you should *ask* OP how he's paying for college, instead of assuming that he's going to incur lots of student loan debt.  (2) 0.1% is insulting, and why my answer recommended Ally Bank.
Comment: @RonJohn I'm assuming nothing, merely pointing out that it's not irrelevant. 0.1% may be insulting but it's not uncommon. You seem to be the one making assumptions about what the OP is doing.
Comment: @Eric he wrote a cogent question, and I answered it.
Answer: Congrats! That's a solid accomplishment for someone who is not even in college yet. I graduated college 3 years ago and I wish I was able to save more in college than I did. The rule of thumb with saving: the earlier the better.
My personal portfolio for retirement is comprised of four areas:
Roth IRA contributions, 401k contributions, HSA contributions, Stock Market
One of the greatest things about the college I attended was its co-op program. I had 3 internships - each were full time positions for 6 months. I strongly recommend, if its available, finding an internship for whatever major you are looking into. It will not only convince you that the career path you chose is what you want to do, but there are added benefits specifically in regards to retirement and savings. In all three of my co-ops I was able to apply 8% of my paycheck to my company's 401k plan. They also had matching available. As a result, my 401k had a pretty substantial savings amount by the time I graduated college.
To circle back to your question, I would recommend investing the money into a Roth IRA or the stock market. I personally have yet to invest a significant amount of money in the stock market. Instead, I have been maxing out my retirement for the last three years. That means I'm adding 18k to my 401k, 5.5k to my Roth, and adding ~3k to my HSA (there are limits to each of these and you can find them online). Compounded interest is amazing (I'm just going to leave this here... https://www.moneyunder30.com/power-of-compound-interest).
Comment: (1) Note that OP can only deposit as much of that $3K into a Roth IRA as he has **earned through wages this year**.  He'll probably need to file a 1040.  (2) Investing in the stock market is orthogonal to whether or not the money goes into a 401(k), Roth or HSA.  (3) He wants to use the money in 4-5 years, not for retirement.
Comment: IMO it's important to be precise.  You can invest ROTH sheltered funds in the stock market, the choices are not mutually exclusive.
Answer: while not stated, if you have any debt at all, use the $3000 to pay it off. That's the best investment in the short term. No risk and guaranteed reward.
College can invite all sorts of unexpected expenses and opportunities, so stay liquid, protect working capital.
Comment: How much debt can a not-yet-adult get into?


Intuition of "Head" in Attention models (Transformer)?

Question: I keep seeing the "head" in attention models (transformers). Aside from the mathematical formula, could anyone please share the intuition behind the idea "head"?
Answer: I like to think about it in the context of progression of attention mechanisms in neural networks.
Early attention mechanisms were implemented as explicit sliding windows over the encoding sequence.  For example, Graves 2013 implemented it as the average of several sliding Gaussians.  So, it was a local attention mechanism to attend to a learnable window over the data.
Then you have Luong and Bahdanau attention, which implemented similar mechanisms, but separate from the network type and as a softmax function.  This is essentially single-head attention.  Now it's not a window, but a score and weighted average over all of the encoding input.  The idea of the K, Q, V flows naturally from that, but in that case the Q is a hidden state of the decoder, and K/V the hidden state of the encoder.  This is more flexible and can attend to more arbitrary windows over the sequence.
Transformers flow naturally from these mechanisms, but now K, Q, V all come from the same sequence, except for the second layer of the decoder, which acts the same as Luong or Bahdanau attention.  In addition, they first split the K, Q, V along their last dimension (the model parameter dimension) to create several heads that can attend to different parts of the sequence.  This is much better at attending to long term and varied parts of the sequence to concatenate an overall context for each Query.  This, of course, is very advantageous for natural language translation, but as we are seeing, it is also great for covering the image space in vision problems.  Intuitively, this makes sense as I view the Transformer as almost a superset of a convolution network, where the filters for each partition of an image attend to various parts of the image and this is learned.
Obviously, there are many papers I'm sure I haven't read and steps in between these.
Answer: A common intuition is viewing attention as probabilistic retrieval: given a query, you want to retrieve some information from some states (values) given some keys that describe the values.
With single-head attention, you get a weighted average of some hidden states with everything that is contained in there. Once you introduce, the head-specific projection, the model has much more flexibility. The information you use for retrieving (in the query-key comparison) can be of a different kind than the value. One head can retrieve a piece of information from some states, another head can retrieve a different piece of information. The head-specific projections also allow throwing away what is no longer relevant for the next layers.


Fridge/freezer door keep closed

Question: Whenever I close the fridge door,the freezer door below pops open. Sometimes it closes by itself but equally it often stays open allowing the freezer to defrost.
I wondered if I could use magnets somehow to keep the freezer door closed.Any ideas?
Comment: Hello, and welcome to Home Improvement. This probably isn't a good place for you to get design suggestions for your need; the answers would be too broad. You should take the tour to see how better to participate here.
Answer: The gasket on the freezer door actually has magnets in it.
Sounds like your gasket isn't making good contact with the door -- either replace the gasket or clean it, or make sure that the hinges are perfectly aligned.
Answer: I have the exact same issue in my apartment. (my gf always does this, and I'm the only one noticing it!). I always thought this was the result of bad levelling. Have you tried tilting the fridge back a bit?
Comment: To clarify, many refrigerators have adjustable front feet or wheel perches. There's probably a nut that can be accessed from behind the grille.
Answer: It would be helpful to know what kind of refrigerator/freezer you are speaking about.  If it is a two chamber commercial unit, so called walk-in the cause could be air pressure from closing the door forcefully passing through any opening between the two areas and pushing the other door open.  Also requires a magnetic type gasket vs a rubber gasket with a positive close latch which would not open if latched properly.  If it is a residential unit then possibly the fridge is not level and closing the door hard is enough to break the magnetic seal.  There are leveling legs under the front corners which are adjustable.

Fridge/freezer door keep closed


Website exit intend detection technology patent

Question: I am making a website code that will display popup when user tries to leave website. Javascript code is used for that. A solution how to detect mouse leave window was published 5 years ago inside Stackoverflow (link to solution). The solution doesn't mention to show popup, it is just how to detect user leaving the site.
What worries me is Bounce Exchange company has a patent to display popup when user leaves window.

Use action in the form of movement of a tracking device on a webpage, represented by cursor gestures on the webpage, is used to detect it a user intends to leave the webpage. Upon detection of an intent to leave the webpage, an advertisement may be displayed to a use.

Patent url
Do you think I can use the solution mentioned inside Stackoverflow for displaying popup? The solution also uses cursor gestures to track exit intend. But it doesn't say anything about displaying popup. So that worries me because Bounce Exchange claims to have a patent of using similar solution to display popup.
Answer: This document is not a granted patent. It is the publication of a patent application. If it is issued as a patent in the future the key will be the wording of the claims, not the abstract or other parts of the document.


Business etiquette on responding to bonus email from CEO

Question: I am a student and have been working part-time in a company. I have never received an increase in my hourly rate, but I received an email from CEO saying that they give me a bonus of $500 from the manager, should I respond to the email by saying thank you?
How should I respond to the email? What is the etiquette?
Comment: Cybersecurity note: If the email has links in it, make sure it is actually legit (by actually talking to your boss, not replying to the email) before clicking on anything. Any time I've gotten a bonus, my manager told me in person, so just getting an email out of the blue sets off a few warning bells for me as a possible phishing ploy.
Answer: We gave our people bonuses pretty regularly. The first time, we might tell them in person or an email. (With long term employees who knew there was generally a financial year end bonus and a calendar year end bonus I might not mention it.) Generally, they said thankyou, and I was never offended by anybody thanking me for a bonus. On the other hand, if they just said "cool!" or "great!" in person without the magic words "Thank you" or if they didn't reply to the email, I didn't hold that against them. Of course, you might work for someone who is a little more petty or in need of validation, who would hold it against you that you didn't thank them.
You can't go wrong with a simple thankyou email. Don't tell them how desperately you needed the money or anything like that, and don't overshare in general. Something like "Thanks, I'll put that to great use" is more than enough. If you want, you could also include a sentence that indicates you understand bonuses mean the company is doing well, and you're happy the company is doing well.
Answer:
Be 1000000% certain it is not a spam or fishing email.

The answer to your question is to reply (A) very briefly (B) remember it "never nurts to be enthusiastic".

"Fantastic, thank you Mr. Smith!"

Done.
Comment: @O.R.Mapper my point was that the scammers would be able to issue orders to the employee, who may carry them out believing them to come from the CEO. In my example above, the scammers were providing a bank account __to__ the employee, and requesting company money be paid into it. This is a thing that actually happens in real life. https://www.fbi.gov/contact-us/field-offices/phoenix/news/press-releases/fbi-warns-of-dramatic-increase-in-business-e-mail-scams
Comment: I don't understand how a scam could come back to bite me here. Surely the worst that could happen is that it turns out I was misled?
Comment: @TonyK The worst that could happen is that the scammers learn that a) your email is active, and b) you think you've got a dialog going with the CEO. "Thanks for the bonus" could be followed up with "I always look after my people. By the way, have we paid the $500k we owe to our external consultants? If not then I need you make it happen ASAP. The bank account number is ..."
Comment: @PlayerOne: Well, an attacker might learn how the OP addresses the CEO, which might then be used in a social engineering attack directed at the CEO. (Giving away a bank account number, on the other hand, may be only a concern in some places.)
Answer: It might depend on how large your company is.
For a small company this likely isn't an issue and will be welcome. However for a large company while it won't get you in trouble it may be unnecessary or unwelcome.
Think about a few things; 1) have you met the CEO, 2) have you had a meaningful interaction with the CEO, 3) would the CEO know you by name if bumped into them at the office, 4) how many employees does company have, and 5) how many employees receive bonuses?
If your answer to first three of these is "No" and the answer to the last two is "a lot", then you may be basically sending your CEO a spam message. If the company has hundreds of employees and  many are sending the CEO "thanks" messages it will clog up their inbox and cause frustration. Just like on SE we avoid thank you comments, answers, and for the most part saluatories in posts. It can become overwhelming to have to sort through all that, even if they go straight to the trash folder.
If your answer to first three of these is "Yes" and the answer to the last two is "not many", then the email will probably be appreciated. However, it may also be better just to thank them in person as well.
You also mention that the bonus is "from the manager". In that case it would be a better option to thank the manager as they are likely responsible for you receiving the bonus. Larger companies tend to have a certain budget for bonus types that managers submit for. While the CEO likes to send out the company wide email, they may not have had a real hand in you getting the bonus. Sending the email to your manager will also let them know you did in fact receive or were approved for the bonus they submitted for you.
In all cases where you do send the email, keep it short and positive.
I would say more than a one line "thank you" but not more than two or three sentences. Something along the lines of "Thank you, Mr. CEO. I appreciate the recognition and look forward to another productive year."


Removing a wax finish from a wood countertop, in preparation for tung oil

Question: I have a wooden countertop in my kitchen that has been finished with Butcher Block Conditioner (mineral oil and natural waxes).  It is not satisfactory and I am now preparing to refinish it, using tung oil (Waterlox).  However, I have to strip all the wax out of the wood first.  What is the easiest, safest and least toxic way to do this?  Will Citrus Solvent do the trick?  Vinegar and water?
Comment: What would you use as a solvent?  Will Citrus Solvent work?
Answer: Wax is pretty hard to remove, everyone seems to agree about that, then everyone disagrees about the best way.  Here is ONE way.
You can use a solvent, rags, and elbow grease to remove wax.  When you apply the solvent to the wax, you get a liquid with wax dissolved in it, and when you wipe it the mix is absorbed by the rag, and thus removed.  With enough passes of solvent and rag you carry away most of the wax.
For the solvent usually mineral spirits to get off as much as possible, and maybe denatured alcohol for a last pass.  (The alcohol will remove the mineral spirits as well.)
For the rags, try fine steel wool or scotch pads for the first pass, then paper towels.  Use a lot of paper towels.  If the paper towel is dirty it's no longer removing wax it's just moving it around.
I don't recommend using a heat gun, to me that just melts the wax deeper into the wood, but it does make sense to keep the ambient temperature in the room on the warm side and keep the solvents at room temperature, not out in a cold garage or something.
When you think you've removed the wax, let that last pass of alcohol dry then spray the surface with water to test.  If the water beads up, try to remove more wax.  (Note that some naturally oily woods may bead up even with the oil removed so this isn't a perfect test.)
Comment: https://wagwalking.com/condition/tung-tree-poisoning  The tung tree is the source of tung Oil, an oil frequently used as a non-toxic wood finish. Although the pressed oil from the tung tree is non-toxic, the remainder of the plant contains saponins and glycosides that are present throughout the plant, but most concentrated in the seeds.

Read more at: https://wagwalking.com/condition/tung-tree-poisoning
Comment: Tung oil is toxic if consumed by mouth. Are you sure you want to use it for this application? Consider adding more wax rather than using solvent to remove wax. The solvent could be very hard to remove.
Comment: @JimStewart I have not heard that, I was under the impression that tung oil was safe unless someone had an allergy, do you have more info?  BTW my answer is just how to remove wax so although interested in the comment not sure it pertains to my answer.
Comment: I didn't research this. I was basing my claim of toxicty on an incident in 1962 when a friend consumed some tung nuts and had to have have his stomach pumped. But I still think it unwise to remove a product designed for butcher block and substitute tung oil finish.
Comment: @JimStewart, thanks for the info, that is interesting. I am always careful replacing a traditional finish - usually the traditional finish proved best.  However tung oil is common for finishing salad bowls so I think it's probably safe.  Maybe there is something in the meat of the nut, not the oil, that caused your friend's reaction?
Comment: One incident reported here: https://www.accessdata.fda.gov/scripts/plantox/detail.cfm?id=1422


Allow posting of recommendations on your CV

Question:
User can send any number of invitations to write a recommendation via email

Encoded link to write recommendation
Recommender can edit / preview / leave & resume / a recommendation
User approves recommendation and is posted to CV
Comment: There would need to be some kind of identity verification, otherwise you could just write your own recommendations.  On LinkedIn you can only be recommended by other people with a LinkedIn profile.
Answer: SO is not a social networking site, sadly.  You'd have to get recommendations from your peers (ie, other SO users) but the site doesn't really connect people well enough to allow for this.  Other verification systems are doomed to be too much work, or not work at all.
I'd like to see this done, I just don't see how it can be done well.
But I believe that it doesn't matter so much - potential employers, if they aren't impressed with your resume, aren't going to be impressed with your recommendations.  They will ask for recommendations during the interview process.
Keep in mind that reputation, though poor, is merit given by one's peers, and thus is a recommendation as-is.
Answer: Careers is slowly turning into linkedin (at least if all feature-requests are implemented)
I'm not saying it's wrong or right though, I kinda like this suggestion
Comment: I wonder if the SO team wouldn't be better off just integrating LinkedIn into SOC... Synchronization of public resumes has also been requested.
Answer: I would like this, or the ability for myself to upload letters of recommendation that I have from colleagues


18650 battery cells died in the winter weather, can they be restored?

Question: I have 1.4kwh worth of hoverboard batteries for my E-bike that I stored in the garage over winter. They were fully charged when stored. I did not know this was bad for the batteries, I took it for a ride today after letting them fully charge on the charger and they died within a minute. I recharged again and they died again in under a minute.
We had a particularly cold winter this year, I'm guessing they stayed in an overcharged state for prolonged periods of time.
Is there a way to restore them?
Comment: https://batterybro.com/blogs/18650-wholesale-battery-reviews/77975750-how-to-store-18650-batteries-safely
Comment: http://batteryuniversity.com/learn/article/how_to_store_batteries
Comment: If it's gone, its gone
Comment: How are the individual cells?
Answer: Unfortunately not, at least safely. Cycling the cells may help if they are still within safe voltage ranges, but is unlikely to undo any of the damage itself.
The battery chemistry itself is likely damaged. I have often stored batteries fully charged, out of convenience rather than lack of thought, and over time the resistance of the cells increases as a result. I have never had any die to that extent over a single winter, I never store them outside in such a state though.
With respect to your predicament, I would suggest cycling them, and if you have / or can obtain a lipo charger with capacity and internal resistance (as many hobby grade chargers for remote control include), you should be able to gauge the state of the batteries to see if the issue is as bad as it seems. It is possible they have usable capacity for other applications but no longer for high-current applications, like your hoverboard, due to a  large increase in internal resistance, which in-turn, causes the voltage to sag and your battery protection in the board to cut off.
In summary, you are unfortunately likely to be looking at new batteries for the hoverboard, but you may be able to make use of the cells for less demanding applications, if they are not completely destroyed.


Why Grover's search return even distribution with half solution

Question: The image below is the result of finding 4 correct answers from 8 candidates using qiskit. The 4 correct answers I set were 000, 001, 010, 011, but the graph shows the probability is incorrect (the result gives even distribution). Then, I tried on cases with more qubits, and they are all confused on half solution condition. I have no idea about why it occurs.
Comment: You need to give us more details of what you were doing.
Answer: Check out this explanation of Grover's algorithm.
If half the possible strings are solutions, then we start with $|s\rangle$ exactly halfway between the $|\text{solution}\rangle$ vector and the $|\text{not-solution}\rangle$ vector. When we then do the two reflections, we end up with a vector that is $$U_s U_w |s\rangle = \tfrac{1}{\sqrt{2}}(|\text{solution}\rangle - |\text{not-solution}\rangle)$$
i.e. equal chance of measuring a solution or not a solution.
In reality, we don't care about the case where 50% of states are solutions since we can solve this easily via random guessing.


How do software interfaces compare to hardware interfaces in therms of speed and reliability?

Question: The Arduino core includes numerous software interfaces mimicking the hardware interfaces provided by the chip and even extending beyond. My question is, if in a project I can either use software or hardware protocol, what would be the difference in stability, speed and versatility? Is there a reason why hardware interfaces are preferred? Because anyways the protocol is handled by the CPU or am I mistaking something?
Comment: the peripherals can work autonomous, involving the CPU over an interrupt only if needed. for example if you start a PWM the CPU is not involved in pulses generation. if you use external interrupt on pin, CPU is not involved in monitoring the pin.
Answer: In your question you ask about all communication interfaces in general, so the answer will be as general as your question.
Hardware interfaces should always be preferred to software interfaces, though there are situations, where it is a better or needed to use a software interface due to limited resources.

Because anyways the protocol is handled by the CPU

That is mostly wrong. The communication protocol is done by the hardware in most cases, if you use hardware interfaces. Serial (UART) for example automatically sends out the byte, that is placed in the hardware buffer, with the set configuration. It does not rely on any software for that. The same goes for SPI or I2C. The protocol of the interface is handled via hardware.
Though at least for Arduino Core/library users there is more to it, that get's handled automatically. Since the interface hardware is limited, the software have to take care of the resulting or needed data. For example: All the interfaces mentioned above use a 1 byte buffer for the data. The software must read or write this data, so that the hardware can work. If you don't read the byte of data, that was received by the Serial interface, it might get overwritten by the next byte. The hardware cannot provide a buffer, that is generally big enough, since the manufacturer cannot know, how long the transmissions will be. So the interfaces get a 1 byte buffer and the software has to do the rest. For this reason all the libraries use a bigger buffer in their software, that gets filled, when the hardware sends a corresponding interrupt.
So: Hardware interfaces implement the basic interface protocol (how the bits get transmitted) in hardware, thus the software only has to provide and read the byte data. The stability, speed and versatility is only determined by how the manufacturer build the hardware of that interface. This limit is clearly specified in the datasheet and does not change with the code.
For software interfaces, everything is done in software. This also involves monitoring and setting the corresponding pins with the correct timing. In the best case the software can utilize general hardware functions like a pin interrupt, but if it cannot do this, it has to constantly monitor (poll) the pins to receive something. Software interfaces are often called "bit banged", because the software manually pushes out each individual bit with the exact needed timing. That is a tedious task, which often blocks the execution of other code, since the timing often is critical. Especially the timing introduces limits, since doing things in software often involves many clock cycles more, than it could be done by dedicated hardware (consider all the code to poll a pin and the multiple if statements to react to specific situations). For example: When you write data with SoftwareSerial the call to the write function will block, because is manually pushes out bit after bit. Or with SPI: With hardware SPI you can go to incredible clock speeds in the MHz range. You won't every get near that with software, because the software simply cannot run this fast.
Note, that depending on the actual hardware of the used chip, a library may need to implement parts of the protocol in software. For example this is the case for using I2C on an ATtiny85, which does not have full I2C hardware support. Instead the USI (Universal Serial Interface) can be used to implement some functions of the protocol in hardware and the rest in software.
TL;DR

Hardware interfaces lift the heavy duty of handling the low level protocol (transmitting the bits by the needed standard) (which can be rather complex) from the software
The Software then only handles the byte data, not it's transmission
Translating complex protocols from dedicated hardware to software (bit banging the data through simple pins) imposes great limits on speed and reliability.
Answer: Using a hardware interface takes a lot of load from the CPU. Let's take an asynchronous serial interface for example.
With the UART built-in hardware you'll get parallel-serial conversion and back done in hardware. The CPU "just" needs to store the data to be sent in a register. The receiving part is handled completely by the hardware and the CPU "just" needs to look at the "received" flag before reading the data. Or it sets up an interrupt as callback.
If you use a software interface the CPU needs to convert the parallel data to serial with several instructions and, really important, needs to maintain a certain timing. For receiving this might be even harder because of the asynchronous nature of the protocol. A timer might be usable to clock the communication, for example by an interrupt, but this puts a lot of load on the CPU. Certain conditions might make this usage impossible, too.
Now you might think about the issues you mentioned:
Stability: If done correctly both approaches are equally stable, meant as reliable function. If you have more tasks to be done you might not be able to meet the requirements. This comes "earlier" with software interfaces than with hardware interfaces due to the higher load.
Speed: Hardware interfaces can be faster than software interfaces because the hardware is commonly clocked faster than what is possible by software which needs multiple instructions for one step. But speed is always a relative issue. There are libraries implementing USB1.1 via software, and the USB1.1 protocol is both fast and really complex.
Versatility: Software interfaces are more versatile because hardware interfaces are limited in their capabilities. If a hardware interface can't do what you need there is no way to make it do this. Software can do "anything" as long as the CPU has enough time and resources for this.
Hardware interfaces are preferred because they are simpler to use and commonly don't put hard requirements on your software architecture.
Comment: Re "_Stability_": Note that software interfaces sometimes cut corners to simplify the implementation. A software UART will typically take a single sample of RX per bit, whereas the hardware UART would take at least three samples and do a majority vote. It is also not uncommon for a software UART to not check the stop bit, and for a software I2C to not support clock stretching. A hardware port also tends to deliver more consistent timings than a software one.
Comment: @EdgarBonet That's what I meant by "If done correctly..." ;-) A hardware UART might start the reception on the leading edge of the start bit, or use a clock of in example 16x. This may be realized in software by edge interrupts and a highly clocked timer interrupt, which is not purely software to be honest.


In The Hobbit, what were the origins of the Dwarves?

Question: After watching the movies, I was left wondering: where do the Dwarves come from? Do they all originate from the same place, or do they have different "countries"? Also, are the dwarves we meet all related to each other?
Answer: The "God" of middle earth "Iluvatar" did not create them. Aulé, the master of craft and work, created the Seven Fathers of the Dwarves deep beneath an unknown mountain somewhere in Middle-Earth.  He did not have the power to give life to his creations so the dwarves were bound to him.  All other Dwarves are descended from them.
Iluvatar reprimanded Aulé, and as such Aulé decided to destroy the Dwarves. As they cowered and begged for mercy, Ilúvatar took pity on them and gave them true life.

The Seven Fathers awoke in their places in pairs with their wives,
  though Durin 1 had awoken alone. The seven different groups of
  Dwarf-folk originated in the locations where the Seven Fathers of the
  Dwarves first awoke.
  3

I hope this answer your question but for more information I suggest you consult this site, http://tolkiengateway.net/wiki/Main_Page
Comment: @CarlSixsmith Cool! Makes sense. So Ilúvatar took pity *of Aulé*, not of the non-sentient Dwarves, then gave them true life, *then* commanded Aulé to destroy them only to stop him as the Dwarves cowed, with a "Ha ha! Fooled ya! They are already alive, dude!" ;)
Comment: @AndresF. No. Eru says, see how they cower, for I have already granted your wish. He had given them sentience already. I am paraphrasing there.
Comment: "deep beneath an unknown mountain somewhere in Middle-earth" - Mount Gundabad
Comment: I always wondered, how can beings who are not truly alive and sentient (i.e. not merely bound to Aulé's mind) "cow and beg for mercy"? A mindless automaton doesn't beg for mercy. Was it merely Aulé's will begging mercy through his puppets?
Comment: @AndresF. And the voice of Ilúvatar said to Aulë: 'Thy offer I accepted even as it was made. Dost thou not see that these things have now a life of their own, and speak with their own voices? Else they would not have flinched from thy blow, nor from any command of thy will.'
Answer: As far as the second part of your question is concerned:
Thorin, son of Thrain, son of Thror, was the heir to the Kingdom under the Mountain. Fili and Kili were his nephews though Dis, his sister (who, incidentally, is the only female Dwarf named in all Tolkien's works).
Balin and Dwalin were brothers, as were Oin and Gloin. All four were Thorin's third cousins.
Dori, Nori and Ori were also brothers, but were only distantly related to Thorin.
Bifur, Bofur and Bombur were cousins and were descended from the Dwarves of Moria.
Dain, son of Nain, who comes to the Battle of Five Armies with five hundred Dwarves, is the second cousin of Thorin and became King under the Mountain after Thorin's death. According to the books, Dain was still the King during the time of the War of the Ring, but fell defending the body of King Brand (Bard's grandson) when Dale was attacked and the Mountain laid siege to by Sauron's forces at the same time he was attacking Gondor.


What are the variables needed for describing Friction, Elasticity, magnetism interactions in a UI

Question: Preparing specs for developers of 'pull to refresh' and flick gestures. I'm trying to figure out how to spec these out. Compared to defining normal animations like movement with time and distance this is more complex.
Comment: Sounds like you'll want to talk to the devs and see exactly what they need from you so they can do their work.
Answer: I think you are talking about something which is available in jQuery, which they call "Easings" https://api.jqueryui.com/easings/
In this website the movement is communicated using a diagram which animates the movement when clicked. There are variations which include things like bounce and elasticity.
Basically the variable you are missing is the rate of acceleration, which can vary throughout the animation, e.g. start slow, speed up, then quickly slowing down, before bouncing, etc.
Comment: thanks but this is not the answer. already know what easings are. what i'm looking for is more like physics characteristics, which can be felt by interacting with it. example in the physical world would be how a squeezing a rubber ball might feel like compared to squeezing a inflated ball


I'm having some trouble moving MX records to the registrars DNS

Question: I run Google Apps email and have traditionally hosted my own DNS records through my Plesk setup.  It has been recommended to us that we'd more reliably serve emails during downtime if we kept the MX and CNAME listings required by Google Apps hosted at Enom instead of handling it internally.
I have essentially copied the settings from Plesk over to Enom.  The domain itself forwards with no problem, but the MX records, while they seem to be input into Enom without error, never seem to reroute my mail.  If I try to send to the email address I'm trying to route, I get the following error bounced back:
Google tried to deliver your message, but it was rejected by the recipient domain. We recommend contacting the other email provider for further information about the cause of this error. The error that the other server returned was: 553 553 sorry, that domain isn't in my list of allowed rcpthosts (#5.7.1) (state 14).
This sort of error gets referenced a lot with regard to propogation, but It's been two days and Enom updates everything else almost instantly.
Ideas?
Comment: header:  MIME-Version: 1.0
Received: by 10.227.155.70 with SMTP id r6mr4076294wbw.26.1285890102711; Th=
u,
 30 Sep 2010 16:41:42 -0700 (PDT)
Received: by 10.227.157.132 with HTTP; Thu, 30 Sep 2010 16:41:42 -0700 (PDT=
)
X-Originating-IP: [220.127.116.11]
Date: Thu, 30 Sep 2010 19:41:42 -0400
Message-ID:
Subject: test
From: Daniel Horton
To: firstname.lastname@example.com
Content-Type: multipart/alternative; boundary=3D0016e659f7e0cad5b40491829eb=
0
Answer: You might be waiting on the TTL (regardless of how quickly eNom updates their DNS records, the TTL will likely be observed by intermediary systems which have cached the MX record), however, the more likely culprit after 48 hours would be your Plesk settings.
Update:
My apologies - I got the impression from your question that you were duplicating your Plesk settings at eNom for redundancy, though the header you provided would indicate otherwise.
From a review of the headers you provided, it looks like eNom is not returning any MX records - see mx:nativeapps.org at MXToolBox (you may want to keep checking what eNom's nameservers return for your domain as you investigate with their support staff).
Comment: Yeah, TTL was set to 5 minutes when I initially tested.  I've since raised it.  And Plesk mail is turned off completely for the domain in question, as is the DNS since it's being handled elsewhere.
Comment: Thanks for getting back.  It wasn't the TTL, but your comment made me certain it was something with the way Enom does things.  Further investigation revealed that my hostname field (which in Plesk needed the domain name to be entered) needed the @ symbol used in Enom (which is a fill-in for "none" apparently).  I wrongly assumed MX settings would be entered using the same syntax regardless of where I was hosting.
Answer: One comment, one idea:
The comment is that this question is probably better served at serverfault.com or superuser.com (I honestly don't know which one is most appropriate).
The idea is that you should include the full bounced mail headers in your question, and state which exact domain is having this problem. DNS is a public system, so once we know what domain it is, we can look at the information you're publicizing in DNS and tell you where the problem is.
Comment: Well, I'll post the headers here (I'll post as a comment above) just in case it gets answered, but I'll try posting on another site as well if nobody gets back.  Seemed like this was something "webmasters" would find appropriate, but I take your point quite well.  Thanks.


Fuzzy logic vs probability

Question: In reading about fuzzy logic it says that fuzzy logic is different from probability. Can some one please explain how these two differ. How can this be explained to a person with no mathematical background.  Please explain the difference of fuzzy logic and probability with a example that can be understood in general.
Comment: "It says" is not helpful. What says, and give an exact quote, please.
Comment: @sam_rox I get a 404 Error when I try to access the link. Perhaps give us the author, title, and date?
Comment: @ThomasAndrews Sorry I've made a mistake in the post. I want to know the difference  between fuzzy logic and probability.  In this article http://www.academia.edu/772082/Fuzzy_Biology   it talks about fuzziness vs probability. But a different example with more explanatation ould be helpful
Answer: Let's use a simple example of your height.  In probability you would define your height as a particular crisp value such as 72 inches.  You might then discuss uncertainty and say that you are 90% confident that your height is 72 $\pm$0.5 inches.  In probability , you assume that each person has a crisp value of height (i.e. there is a right answer to the question "How tall are you?") and we try to determine how likely we are going to be correct in making statements about these crisp values.  In fuzzy logic, we would describe height using different terms such as "tall", "very tall", "moderately tall", etc.  Each of these sets includes a range of heights.  Tall might be from 68 to 76 inches, "very tall" might be from 73 to 80 inches, "moderately tall" might be from 67 to 72 inches.  So a given person's height might be described by more than one set.  If one was, for example, 74 inches he would be in the "tall" and "very tall" set.  The other thing about fuzzy sets is that set membership is not binary.  In classical logic, an element is either in or our of the set.  In fuzzy logic membership in a set is a continuum, so one can be 40% in the "tall" set and 70% in the "very tall" set.
So to sum up, probability assumes that there is a definite numerical height that we can try to make assertions about, but there is a true value (which may not be known to us).  Fuzzy logic deals with fuzzy sets which cover ranges of values and are not mutually exclusive.
Comment: How would you compute that someone is 70% "very tall" from real data without using a probability measure?
Comment: Their actual height when evaluated by the "very tall" membership function would yield a value of 70%.
Comment: Okay, let's say that $f_{\text{very tall}}(h) = 70$. For pure math purposes it is enough to say that such a mapping exists. In what sense does 70% correspond to data or observables? Where does such a number come from other than arbitrary assignment?
Comment: The closest I have found to answering these questions is [fuzzy clustering](https://en.wikipedia.org/wiki/Fuzzy_clustering) but I am not sure that there isn't a probability interpretation lurking in algorithms like fuzzy c-means.
Answer: On a theoretical level, it goes back to Aristotle's Law of the Excluded Middle that states a statement must be either True or False.  This is one of the axioms (foundations) of probability.  It is seen but the equation P(f) + P(t) = 1.  This is also shown in "crisp" sets in which some object is either a member of a set or it is not.
This works well for things that can be empirically measured.  But falls apart when trying to deal with non-empirical things, the best example being natural language. Here there are gray areas.
For example a grading scale often used 90-80-70-60. After tedious arguments about rounding,etc, an empirical line is drawn. Grades > 90 are A. Grades < 90 are Not A. This is pretty much how things work.
However, this falls apart when linguistic terms are used.  Assume the highest category is "Superior".  Empirically a 90 is "Superior" but an 89.999999 is not which is not an accurate reflection of the reality that both students are the same.
FINALLY,  in fuzzy logic the two students would receive several "Possibilities". There is a 1% chance that one or both are "Poor", 25% chance that they are Average, 50% chance that they are "Above Average" and a 50% chance that one or both are "Superior".
Notice that the possibilities do not add up to 100%. MAYBE (a term not allowed in probability) one or both are Superior and MAYBE one or both are Above Average. There is a very small POSSIBILITY that one or both are poor and it is POSSIBLE that they are Average
Then there's some mathematical jujitsu to "Defuzzify" the score to a single number if needed.
Answer: Fuzzy logic and probability theory are two independent sources of indeterminacy in judging if an element $x\in A\,$ is in a set. If $\,x\,$ is precisely known and $A\,$ is clearly defined, then $\,x\in A\,$ is either true or false, following the "law of excluded middle". This is how classical logic works.
Probability theory points out one way to turn the answer into a "maybe". If the value of $\,x\,$ is not known exactly (or not known at all) but we only have a sense of what values are more likely than others, then we can describe what we know about the value of $\,x\,$ not using one particular real number, but using a distribution over the possible real numbers to tell how probable they are. An example would be throwing two fair dices. The sum $\,x\,$ of the points would be more likely to be a $7$ than to be a $2$ or $12$ simply because there are more ways to get a $7$.
Fuzzy logic offers another way to have a "maybe" answer $-$ if the set $A\,$ is fuzzy. Still using the dice example, if we consider events like "$x=7$", "$x>9$", "$x\leq 3$", "$x$ is odd", "$x$ is prime", etc., we find that the only indeterminacy is that we don't know $x$. Once $x$ is known (e.g. after you throw the two dices), whether these events happen or not are clearly defined. Now consider this event:
$$x\mbox{ is big.}$$
This time, even if the value of $\,x\,$ is given (e.g. $x=10$), whether it is considered big is not clearly defined, because the set of "big numbers" is fuzzy. $x=12$ would impress almost all of your friends in a party; $x=11$ may  still impress the majority of them; $x=10$ may impress only half of them or less, and so on. So every point sum $\,x\,$ is "big" to some extent. For some $\,x\,$, the truth value is close to $1$ (e.g.$\,x=12$), and for some $\,x\,$, the truth value is close to $0$ (e.g.$\,x=2$).
Comment: Isn't this example of "$x$ is big" still a probability problem? You speak of the fraction of your friends which are impressed over the possible values of $x$, which would be a frequentist probability measure.
Comment: @Galen in that case you're defining the probability as "The chance that any randomly selected friend would say that x is big", right? Which seems different from "What is the average of all your friends' opinion of whether x is big?"
Comment: @naught101 Specifically in response to the above answer, yes, their description in the first part of the last paragraph is clearly ratios of friends conditioned on the outcome $x$, which in terms of probably might briefly be denoted as $Pr[\text{x is big} \mid x]$. The last part of that same paragraph appears to change from that frequency perspective to fuzzy description, which is different, and hence my original comment.

Fuzzy logic vs probability


CEO says not to expect pay increases unless you do something really exceptional. Is this counter-productive?

Question: Our CEO has recently said we should not expect pay increases (above the usual yearly inflation adjustment) unless you're an overachiever or do something really exceptional. Is this counter-productive for staff moral, retention, and productivity or should it be taken as a challenge to do better?
Comment: Is this an exceptional company with exceptional people and an exceptional CEO? Then, perhaps, it will help productivity. But if a normal person is told that they are going to play the exceptionality lottery with exceptionally low winning odds, why should they try?
Comment: Did you CEO promise exceptional raises for exceptional work? Or just normal ones? Or was it not mentioned. I mean, are you collectively going on an all or nothing viking raid to cover yourself in riches, or are you just going to bust your asses for megre returns. How was this sold?
Comment: Be careful: In some countries, inflation measures do not include rent, and therefore severely underestimate the actual increase of regular expenses households are making. So even if they increase it "only by inflation", depending on how inflation is measured, you may still lose real income.
Comment: One wonders if this cap on increases in total compensation also applies to senior management. Perhaps you could ask how much senior executive total compensation -- not salary; salary is peanuts to executives -- increases year over year, and what "exceptional" behaviours justifies it.
Comment: @davnicwil it certainly is an `interesting question on management, economics, strategy etc in the workplace`. Specifically, it's an interesting question seeking **opinions** about these workplace issues. It doesn't have a problem it seeks to solve and primarily opinion-based questions are off-topic here.
Comment: Who decides if and when your work is exceptional?  and how?
Comment: @JoeStrazzere I think the problem here is that it's hard to quantify what "exceptional" means since it hasn't been said what metrics this would depend on  and it is very subjective. I felt it was quite a demoralising statement but perhaps it's not what others see it as, I guess my questions was more to do about if I was taking the comment on-board correctly as I was not sure what to make of it at first (I've edited my question to reflect)
Comment: Actually the fact that the salaries are being regularly adjusted for inflation makes it above average in my experience. Every place I've ever worked, inflation adjustments were still called "merit increases".
Comment: I would but I either don't know how or simply am not allowed to.. :)
Comment: @KDev Even if metrics are supplied don't trust them at face value. If there is more than 1 measured value it can be easy for management to overlook 1 value and focus on a different specific measured value. I once had a manager who would barely mention the fact that I was performing above and beyond expectations in most areas, and he focused an employee review almost entirely on the fact that I had 5 or 6 late timesheets that year and rated me poorly. Mind you, "late" included 20 minutes **before** the deadline time because that was "cutting it too close"
Answer:
Is this counter-productive for staff moral, retention, and
  productivity?

Yes, it is.
People generally get better at their jobs with more experience, and if their productivity increases, they expect to be compensated for it.  If it becomes clear that won't happen at this job, they'll start looking for some place where it will.  The very best employees, if they're getting really good pay increases, may stay, as well as the very worst, who are just lucky they haven't been fired, but a large number of those in the middle will leave.
Comment: Dilbert's boss gave out new titles, not raises, for exceptional work. "It's how we recognize our best employees". Dilbert: "I thought out best employees left for other companies." The Boss: "That's the other way to recognize them."
Comment: It's not just that they leave, it's also that they have no incentive to increase their productivity while they are still there.
Comment: @Allure getting more productive as you gain experience is not the same thing as being an overachiever, an overachiever is someone who goes above and beyond what's expected of them to deliver exceptional results.
Comment: Comments are not for extended discussion; this conversation has been [moved to chat](https://chat.stackexchange.com/rooms/101187/discussion-on-answer-by-joeqwerty-ceo-says-not-to-expect-pay-increases-unless-yo).
Comment: *if they're getting really good pay increases*. It really depends on whether this is an up-or-out thin-out-the-heard thing or whether you have a begger-ceo who wants to pay normally for the exceptionally and pay badly for the normal. We can't know.
Comment: Not a fan of this answer. Note the question says "...unless you're an overachiever". If people become more productive as they gain experience, then they become an overachiever.
Comment: @Eloff I do not interpret it that way - overachiever means achieving more than one's peers, and if experience matters then one will eventually be overachieving.
Comment: @Allure Gaining experience is normal.  I would normally expect an experienced person to achieve more than an inexperienced one.  However, that is not a fair comparison in relation to overachievement.  An experienced person can be both an underachiever (in relation to other equally experienced people) while also outperforming an inexperienced person.
Comment: @allure If "people become more productive as they gain experience", and if a particular individual becomes more productive as they gain experience, then they have merely done what people generally do, so that does not make them an overachiever. To be an overachiever they would have to gain productivity *on top of* what would normally be gained from experience.
Comment: @JonBentley precisely, which is why they should not expect pay rises at a rate faster than inflation. I see how what I originally wrote is misleading, though. Unfortunately I can't edit it anymore.
Comment: @JonBentley let's take this to the chat room linked above.
Answer: Are employees becoming more valuable to the company over time?  For example, do they tend to develop skills that make them more productive or maintain relationships that bring in business?

If so, it'd make sense to increase their compensation over time to reflect their increasing value.  Otherwise, it'd seem like employees would leave to pursue better-paying positions elsewhere, while the company would develop a reputation as a lousy employer.
If not, then it could make sense to not raise their compensation much over inflation.  Then if/when employees quit, the company can just hire new employees of the same value at the same rate.  The company may want to take steps to avoid too much turnover, but constantly increasing an employee's compensation over their expected market value would be hard to justify.

Also, I'd question the use of raises as rewards for exceptional work.

If an employee's exceptional performance proves that they were more valuable in the past than their compensation reflected, then a bonus could help rectify the misalignment.
If an employee's exceptional performance suggests that they will be more valuable in the future than their scheduled compensation reflects, then a raise could help rectify the misalignment.
If an employee's exceptional performance reflects misalignment in both prior compensation and future compensation, then both a bonus (for the past) and a raise (for the future) could help rectify the misalignment.

In general, I'd be dubious about an employee's planned compensation deviating from their expected value.  So, employees ought to receive raises for both their expected increase in value to the company (e.g., due to increased experience) and as adjustments due to them proving to be exceptional performers, while bonuses would seem more appropriate to reward employees for past performance (considered separately from updated projections of their future performance).
Comment: Exceptional work deserves exceptional pay (i.e. a bonus). A consistent pattern of better work deserves a consistent pattern of better pay (i.e. a raise).
Comment: A classic example is food chain cashiers. Since you the business can get new ones for minimum wage and their learning curve is short they will be paid minimum wage.
Comment: @Nat The company develops and supports retail software so yes overtime employees do become more valuable as they acquire specific knowledge and skills to cater to the industry. A new hire could take a few weeks before becoming productive depending on their skill level. A bonus scheme has been implemented though it is fairly convoluted in terms of the formulas used to calculate bonuses and employees are only entitled to it after a certain time at the company.
Answer:
unless you're an overachiever or do something really exceptional

This is arbitrary. In reality it means the CEO is unwilling to give raises and is telling everyone not to ask him. He's just putting it in a nice way to avoid confrontation and since he's arbitrarily stating what he wants, he could form fit it into anything. "I put in 20 hours of extra work a week for the last six months to push this product out in time. I want a raise" "Well sorry Jim, but this is expected of you to put over time in and thus, I cannot give a raise."
I'm sure it would cause people to want to quit, but I don't think so unless someone feels like they are putting in a lot of extra work in hope to get a raise. I suspect that this will cause turn overs but not immediately. Assuming the average person is paid within a +/- 10% of the market rate for the area, I suspect the CEO will get about 4-5 years worth of work from that person before they expect to get a raise that will cause them to leave. That's assuming the position is competitive like an IT position where as someone matures in his/her career, they become more valuable. I also suspect that people will find new hires getting paid more than they are as the years go on. In my last job, I was a victim to both of the above: I was underpaid by 25% because I stayed in longer than I should, but at the same time, new hires were hired on at a higher pay that I was getting when I first started and thus, "beat me" in terms of yearly cost of living increases.
Comment: If it's _not_ something competitive like IT then I'd expect it to be 4-5 years - otherwise I'd expect someone to leave within 2 years due to policy like this, and possibly as soon as 1 year if they perceive that the policy is likely to affect their future earnings.
Comment: I'd expect the CEO to not care, either. At the job I described, they regularly joke about people leaving. They call it a changing times and they just expect that people will leave and they'll continue to hire folks. They are getting better at employee retention but overall people quit in large numbers as they realize their careers are stale and they become uncompetitive in the marketplace.
Comment: The cynic in me says this is the right answer.
Comment: @LoganPickup You're right as most lateral positions will ask for salary information. If you currently make 30% under, you're unlikely to get matched to what you want. I also suspect as people realize new hires are getting paid more than they did when they started, they'll quit in anger unless there is a larger gap or pay raise between their current amount.
Answer: Lying is counterproductive
It's reasonable to assume that this is an accurate description of the current situation - that the company fully expects to keep its salary budget per headcount the same (given the inflation adjustment) and the budgets allocated to smaller units and middle management reflect that.
So what we're discussing is actually about the advantages and disadvantages of openly admitting this policy, instead of misleading employees - which is often done. We have many questions on this site about the harmful consequences to "staff moral, retention, and productivity" resulting from management falsely implying that raises would be upcoming, and (intentionally) failing to deliver.
Of course, allocating more resources to staff probably would facilitate morale and productivity - however, if the situation is what it is, I'd argue that lying about the situation would be far more counterproductive than honest, realistic information.
Comment: This is a good point. If there is in fact no money for raises above inflation, it may be better for the CEO to be honest about it. Doesn't mean people won't leave though.
Answer: In a lot of countries money loses its value over time due to inflation. For example, Swedish financial politics have a set goal of 2% inflation per year. This means my salary will be worth about 2% less next year unless I get a raise.
So should you expect a raise? I would expect a base raise of 2% per year because otherwise I get a pay decrease meaning the company values me less every year. I would also expect more than that because my increased experience should be valuable in itself. This is given I have the same duties as last year.
Do you have a personal development plan set together with your manager? You should have goals about things to improve every year. If you meet these, you are also more valuable than last year.
Your employer does not see it this way. They already communicated that they believe you are worth less to them every year unless you are "exceptional", whatever that means. Most people are behaving within the constraints set by their managers and don't have much playroom to do anything else.
Personally, I am valuable in the work market at the moment so I would consider this a huge red flag and start looking for other opportunities. Only an exceptional employer is worthy of my time.
If you want to stay and try to be exceptional, make sure you have a meeting with your manager where you write down what you are good at and set goals for the next year. The goals should be specific, measurable and realistic. Meeting the goals should be worthy of a raise.
Comment: The OP clearly states "`we should not expect pay increases (above the usual yearly inflation adjustment)`".
Comment: No, the company loses 2% unless they raise their prices to match the inflation. The raise is not a loss of real income, it's preserving the real value.
Comment: I don't know about Sweden, but in the UK, the commonly used Retail Price Index (RPI) inflation measure explicitly does not consider rent, which makes it pretty useless when the expense that may well compromise 50% or more of household income in a city like London increases by 5% per year.  So when they "adjust by inflation", read the smallprint.
Comment: @jwenting: You seem to have a entirely distorted view of inflation. Inflation affects all prices: parts bought, wages paid, and goods sold. If things are right, the price of goods sold exceeds the price of parts&labor, so there's a profit left. If all prices rise by 2%, profit rises by 2% as well.
Comment: How can tax increases be "left out of the official documents?" If taxes are increased, surely that's reflected in both government documents, which would show an increase in the tax rate, and corporate financial statements, which would show an increase in the effective tax rate paid by the firm?
Comment: @jwenting: I would describe your tax view as "unorthodox". The ECB thinks interest rates are the primary driver of inflation, and uses that view to justify negative interest rates. The chief problem with your view is that governments tax business profits, which are a "below the line" number.
Comment: @Myles That's what happens when I give benefit of the doubt. Going to flag this whole comment thread too.
Comment: @jwenting Control of the money supply is not a purely Keynesian idea, in fact it was heavily supported by Milton Friedman (who advanced Monetarism and was very much against Keynes's ideas for dealing with recessions). Beyond that, economics after 2008 has revived Keynesian ideas, as "New Keynesian economics", and even "Classical" economics has been forced to incorporate some, turning into "New Classical" economics. Calling it "discredited" is rather silly.
Comment: @MSalters That's not entirely true. What's usually quoted as inflation is the rise of prices in a selected bunch of things the statistics come up with. This is essentially arbitrary at best, and usually tuned to fit the government targets for what inflation is "supposed to be". It's not _all_ the prices increasing by a flat 2%, nor is it the _average_ of all prices increasing by 2%. It's yet another meaningless number that governments love. That said, jwenting's view is not just "not entirely true", but just flat out wrong, as you point out :)
Comment: @DJClayworth  If you look at the edit history the mention of inflationary raise is part of the original question.  Seems like the person providing this answer made no effort to understand the full two sentences of this question.
Comment: Actually it makes more sense for your salary to rise in line with an earnings index than an inflation index. In this way you can buy *more* things than you could before when standards of living generally are rising, and you can buy *less* things than you could before when there is a recession (both of which are fair and reasonable). If for example, the earnings index has increased by 4% and inflation by 2%, and you get a 2% pay rise, you income has effectively gone *down* relative to the growth of the economy, despite that you can buy the same things you could before.
Comment: They have to raise prices by 2% even if they do not give you a raise in order to prevent losing money. If they also raise your salaries by 2% they have to raise prices even more... The inflation rate is mostly determined by taxation, and companies counter that by raising their prices.
Comment: @gerrit and in the Netherlands it does not include increases in VAT and fuel taxes, which are a major factor in the reduction in purchasing power by citizens.
Comment: @MSalters utter nonsense, and self serving statements by the ECB, who are blindly quoting Keynesian economics which have the government "steer" the economy through increasing and decreasing the money supply (in part through interest rate manipulation). Keynes has been thoroughly discredited long ago btw.
Comment: The question now says "should not expect pay increases (above the usual yearly inflation adjustment)" so the first part of this answer no longer applies. And virtually all of the discussion is irrelevant.
Answer: Yes. It's counter-productive. And yes, it's also a challenge. It just depends on the mentality of the listener.
On one end of the spectrum, those who come to work with the mindset of accomplishing the minimum requirement and complain about the smallest thing that comes up will find it upsetting, demoralizing etc... alongside things like the fridge is one degree colder or warmer than it should be, office lighting is too bright/too dark etc.
At the other end are folks that have the mindset of "I want to contribute something" who will read the message as contributions above and beyond what's expected can get rewarded.
Comment: `those who come to work with the mindset of accomplishing the minimum requirement and complain about the smallest thing that comes up will find it upsetting, demoralizing etc...` - It's also demoralizing and upsetting if you don't complain about the small things -> you're spending your valuable time and brainpower learning the companies' processes, business, colleagues, quirks, market, competition, customers, etc., next to what you were hired to do: the job. You should expect a payrise for being more knowledgeable, and by proxy more efficient, as time goes by.
Comment: If the idea of the CEO here also includes exceptional raises for exceptional people, then this is a good answer. If the CEO mostly wanted to communicate that there are not going to be any raises, the advise is bad. This requires more info from OP to judge.
Comment: I come to work wanting to contribute. But I realize that I am unlikely to contribute something 'exceptional" because all my colleagues feel the same (that's what I like about it). So it still comes down to "only a few of us are going to get pay raises".
Comment: I agree with you wholeheartedly. I would never expect a pay rise unless I'm going above and beyond the call of duty. To me a pay rise is earned and shouldn't be expected for merely turning up and doing the bare minimum.
Answer: Not only is this policy counterproductive, but it's actually a great way of losing the talent that the CEO is trying to reward!
Imagine a basic entry-level job that pays $100.  After a year of 2% inflation, what do you think the same entry level job will pay for someone just starting?  Or someone starting ten years later?  The salary will go up - but it's not like the company is paying "more" - it's just that the currency they're using is worth a bit less.  It's why the entry level salary for a [Insert-Occupation-Here] pays more than it did back in 2000.  Or 1990.
So you might start to see the problem.  If the entry-level position is going to be paying 2% more next year... and you're going to be giving out a 2% raise for the people already working there - you're effectively still only paying them entry level.  Paying people "inflation-only" raises implies they're worth the same amount to the company after working there a few years than when they first started.
But here's where that gets worse.  Bob Bobson, the lazy IT computer repair tech?  He probably didn't improve all that much the last 5 years he worked there.  Sure, he knows a few tips/tricks around the office and a few common ways devices fail, but he's basically adding the same amount of value to the company when he started.  Bob, with his inflation-level raises, is still getting paid roughly the amount he's worth.  Bob probably won't get much out of switching companies.
But Alice the IT tech?  Oh, she works hard.  She learns all she can.  She's become an expert in google, she's getting really good at troubleshooting new problems, and has become really good at translating "user speak" to "technical speak".  Alice's value to the company has skyrocketed.  And, more to the point: her value to anyone else that wants to hire her has also skyrocketed.  Alice, if she were only getting Inflation-Based raises, would have a huge financial incentive to jump ship.
Charlie, on the other hand, is in between them.  He does a decent job.  He's much better at his job than when he started - he gets things done faster, more reliably, and with better customer engagement.  He's worth more to the company (and to competitors) than when he started out.  So he's also got a financial incentive to jump ship (just not as large of one as Alice.)
That's why what the CEO is doing is so stupid.  They're trying to incentivize talent... but all they're likely going to accomplish is push out the best talent by giving them a financial incentive to leave.  The mediocre employees are going to be the only ones to stay - because they're the only ones worth roughly the same as when they started.
Comment: Alice *might* get a raise for her exceptional work, but Bob and Charlie have no incentive to improve because they won't be rewarded. Eventually the company ends up with Bob running a department of newbies, who don't stay long.
Answer: Bonuses or commission are more usual mechanisms for this kind of thing.
i.e. You get your salary for doing your job, and there's an expected level of value you deliver there. Then you get bonuses for specific extra things you do on top to deliver any tangible extra value.
There are issues with motivating such things with salary increases, simply because salaries recur. That makes it difficult to separate the reward you get for specific extra value you deliver, from your job's ongoing market salary. This means that the rewards can be unfair, or raise other issues related to salary in the long term, which is indeed bad for staff morale, retention, and productivity.
One example

Your colleague does something great in year 1, gets a 10% raise, you get no raise. Year 2, you do something even better and get 15%, your colleague gets none. Year 3 you get 5%, your colleague gets 10%. In aggregate over time you're excelling at around the same level, nevertheless your colleague is better off than you just because they were first.

Another

You do something extra that delivers 2X of value, then get a raise of X. You have a salary 10X - so a 10% raise. Your colleague also delivers 2X of value, but their salary is 4X. When they get a raise of X, it's a 25% raise. Is that fair? Ok, so make their raise less. But then you've been rewarded more for the same thing when you already have a higher salary. That's definitely not fair.

Another

Let's say raises aren't particularly common, you have to really excel to get one. A colleague gets one in year 1 while no team mate who is paid similarly does. This colleague never again repeats that exceptional performance. Now they're making X% more, doing the same job as everyone else, without having the ongoing better performance to justify that. That's not at all fair. Worse, what if the policy is later dropped and teammates lose any chance at all of ever catching up?

If you have the kind of relationship with your CEO where you can openly discuss these sorts of things, it might be worth mentioning this, as they might not have thought about it and seen any potential negative consequences.
Bonuses and commission have their own issues, of course, but they (and not salary) are the more standard way of doing this for a reason, and it might be worth thinking about that.
Comment: "Bonuses or commission are more usual mechanisms for this kind of thing." I don't know about jobs with commissions, but the several places my wife and I have worked with bonuses have always given said bonuses in conjunction with appropriately large raises (i.e. higher than inflation).
Answer: We can talk whatever we want, but it all comes down to supply and demand in that place and time.
If the employees can find, in the same country and city, a better job (more paid, or better in other ways), they can prove the CEO wrong.
If they cannot, if there are no better jobs for the same level of skill and productivity, then the CEO is right.
However, even in the case they cannot find it now, the situation can change. So, it's good for each side to not annoy the other side too much, because if the situation changes, they might all of a sudden find themselves with a big problem on their hands.
If you do things because you can, because the other side for whatever reason cannot stop or punish you, once they can, you will be dealing not only with reaction to the current issue, but also with reaction to all the years of accumulated frustration.
Answer: It is not counterproductive IF the same rules also apply to the CEO and the board of directors.
Almost by definition, none of those roles allow them to carry out anything exceptional. If the company makes a successful profit, that is merely them carrying out their job normally. If they are seen to be taking pay rises, dividends, stock options or any other extras whilst holding down pay for everyone else, morale will tank as expected.
A further requirement for it to not be counterproductive is if the same rules also apply to the company owners or shareholders. If the company has had a bad patch, it's normal for there to be some salary stagnation. If the company is making a healthy profit though but refusing to adequately reward their employees, then their employees will leave.
So it is somewhat conditional.
Comment: @dwizum Nope, they're paid a dividend which is not necessarily related to profits. But even insofar as it is somewhat linked to profits, that profit is money which could have given someone a pay rise. The CEO has made this a zero-sum game, in other words, and it's not in the employees' interest to work harder to make the company more successful when the only benefits go to the owners or shareholders.
Comment: @dwizum The point is that over time employees *do* become more valuable to the company and so *do* deserve a greater-than-inflation pay rise as a matter of course. The only way this can be justifiable is if the company is in a financial situation where they can't afford it. If the owners are extracting plenty of profits, then they and the CEO are directly and explicitly abusing the trust of their employees. Remember that the OP asked for how this could be acceptable. If the owners are still taking large profits whilst squeezing salaries, then that fails the OP's test.
Comment: *A further requirement for it to not be counterproductive is if the same rules also apply to the company owners or shareholders* huh? Owners and shareholders - by definition - are "paid" the profits the company makes, not a salary that is subject to discretionary or arbitrary raise policies.
Comment: If the employees want direct access to profit, perhaps they should consider becoming investors. Otherwise, why should they expect anything different than a salary? Profit is tied to risk (the risk of investing and potentially failing), not work product. Work product is compensated by salary. Claiming that owners and workers need to be paid based on the same model doesn't make any sense to me.
Answer: The CEO appears to be assuming that other similar employers in the area are only giving inflational salary increases (on average) and that the salaries for staff in their industry are increasing in line with inflation.
That may be the case (I am not familiar with the specifics of your industry/job market). However, if it is not and salaries in the 'market' are increasing faster than inflation, then it is a bad strategy. Because, in time, the salaries your company is paying its employees will fall behind other similar employers in the local area and many employees will leave to go to places where they will earn more (at least, the best ones will). Sooner or later, the company will also start having more difficulty hiring new employees, because it will not be offering them a competitive salary (unless they pay new staff more than legacy staff, which is inherently unfair and not rewarding loyalty).
Salary increases are not just about rewarding staff, they are also about keeping up with the market value of your employees, so you can retain/attract the best talent. In my opinion, your CEO should be more concerned with keeping salaries in-line with current market value, not necessarily tracking inflation.
Of course, if he wants to attract and retain the best talent, then he may want to consider offering above the currently-perceived market value. (that is where inflation actually comes from, after all ... i.e. competition)
Comment: In addition, there's the factor that 'raises' are evil in the eyes of management, but normal for hiring people.  If a competitor is willing to hire for a 15% bump, that's more than employees at the first company will get in many years.
Answer: No, from the CEO perspective. And properly run methods of measurments of employee "productivity".
A pay increase, above inflantion, should be a reward for doing more than you are paid for. If you are hired for X amount to do Y stuff then if you do Y+C your pay should also reflect that.
If you do that extra C once then you should get bonus.
If you do it constantly then you should get a raise
OR
you company should evaluate your performance and decide if maybe they should hire another employee.
It make sense when your performance is something you (as you and employeer) can check and measure: Key Performance Indicators, Touchdowns, Tasks, Objectives etc.
Then you know what you're supposed to do and see things you can do better. A place for improvement.
If this is wrong for morale? Only for people who would like to get rewarded for doing things they are already paid. So it help company weed out the ones who are not willing to do something extra.
Comment: Most people become worth more after they have a year's extra experience doing something. They don't have to be "exceptional".
Comment: @DJClayworth Most people are hired based on tasks they should do not their worth. You learn how to do something faster/better? That's the exceptional work. YOu do something the same? Where's the increase in worth?
Comment: You say "no" and then argue "yes". A properly run method of measurement measures all improvements (I agree with that), not just exceptional increases (which the CEO wants to measure)
Comment: @MSalters I mean "No" as in "from a CEO POV it's not counter producitve". I also argue that it make sense only if you measure all improvements because only then you can get information about exceptional ones.
Comment: By "worth" I mean "value to the company". And learning to do something faster or better is not "exceptional". Most people do it in the course of a year.  That's the problem. Most people will be improving their value to the company, but only a few will be getting pay raises for doing it.
Answer: This is fine, as a temporary situation, if and only if the company is in a recession. In such a situation it means "we don't have money for pay raises, but for those who truly deserve one we'll reserve the right to make an exception.".
It's also fine in a low skill industry, when the company expects rehiring and retraining to be fast and cheap, and experience to be valueless.
In situations where people's experience and market value are correlated - and alternative jobs are available - such a policy would be expensive, because it would force all workers to leave the company after a few years in order to get a pay raise.
Comment: The health of the company doesn't matter, as employees can always leave for a healthier company. It only makes sense in a national/global recession when they can't. (or a low-skill industry, as you say). Unless perhaps the CEO promises double raises the following year.
Answer: Flipped around from the other perspective this would be like you telling the CEO, "don't expect productivity increases unless you pay something really exceptional". Expressed that way is damaging to the relationship also, but makes it more apparent why...
In general, one should steer clear of taking a hard line on the terms of the relationship, unless there is a willingness to increase the risk of the other party walking. I think in this situation, the CEO has upped the risk of their employees starting to look elsewhere.
Answer: The word "overachiever" can have different interpretations here, and the answer can be different because of that. I discovered this in a chat with JBentley (thanks!).
To illustrate let's suppose that two people, Alice and Bob, are both fixing cars. The company expects new hires to both fix ten cars a day. As they gain experience, in one year's time, the company expects them to be able to work faster and so fix eleven cars a day. Alice has worked for a year while Bob is a new hire, so Alice is faster than Bob.
In the first interpretation of "overachiever", Alice is overachieving - she fixes more cars than Bob and is therefore worth more. In the second interpretation, Alice is not overachieving - she's simply achieving what is average.
I'll venture that under the first interpretation, your CEO is being quite logical. Experience is not worth much if it doesn't lead to an improvement in productivity. Under the second interpretation however, your CEO is not being fair, because Alice is obviously worth more than Bob to the company (she's fixing one extra car a day).
Ultimately what you and I think is the correct interpretation doesn't matter; what matters is what your CEO meant. It's not something I would be comfortable asking about. If you can draw conclusions based on indirect observations, I would suggest doing that first.


Exact sequence of sheaves of holomorphic functions

Question: This is from Exercise 2.4.P. June 2013 version of Ravi Vakil's Math 216 notes.  The idea is to show $\mathscr{O}_X \xrightarrow{\text{exp}} \mathscr{O}^*_X$ is an epimorphism.  It seems straightforward to show surjectivity of stalks by invoking the fact that the logarithm exists for simply connected components.  I'm wondering if there is a more categorical approach I'm missing?
Comment: Why should there be a more categorical approach? This is a property of a very specific morphism.
Comment: I agree with Zhen Lin. The question doesn't make much sense ...
Comment: I don't even know what «more categorical» might mean in this context :-)
Comment: I guess I should clarify...  I was thinking of something along the lines of deducing a property of the $\mathscr{O}_X$ and $\mathscr{O}_X^*$ categories and then saying using something along the lines of "for any sheaf morphism from $\mathscr{O}_X$ to some object $A$ there is at most one commuting morphism because..." instead of using the stalk properties.  Given the flow of the book and the comment immediately after the problem, it struck me as the way to start approaching the problem.  It seems the consensus is that I didn't miss anything simple and am now just being dumb :(
Answer: Don't use stalks, use the following characterization of epis of sheaves: Every section in the target admits a covering such that each restricted section has a preimage in the source. Here, you only need the trivial direction that such a morphism is an epi. Therefore, the existence of local logarithms is precisely what we need. You cannot get this for free by abstract nonsense, because somewhere we really have to use that we are looking at the exponential function.


Is there a single word for emotional baggage?

Question: ie. Barry couldn't go to such and such bar anymore because it reminded him of where he met his first love that didn't work out and he had to much emotional baggage
Comment: A few verbs spring to mind rather than nouns. But I would rewrite from scratch. It's a clumsily written sentence and fixing just one word in it won't make it less clumsy. (Nota bene: "i.e." is not the same thing as "e.g.". Just like "to" is not the same thing as "too".)
Comment: Possible duplicate https://english.stackexchange.com/questions/258856/a-word-meaning-to-remember-emotionally-or-sadly
Comment: "Bullshit" comes to mind. If you are trying to write in English, focus on the ideas you wish to express and try to state them simply and clearly. You should be working with formulations such as "…because it invoked bitter memories of his shattered first romance". And you mean eg, not i.e., and sentences end with a full stop / period.
Answer: This is what Wikipedia says about emotional baggage:

Emotional baggage is an everyday expression that correlates with many varied but similar concepts within social sciences, self-help movements, and other fields: its general concern is with unresolved issues of an emotional nature, often with an implication that the emotional baggage is detrimental.
As a metaphorical image, it is that of carrying all the disappointments, wrongs, and trauma of the past around with one in a heavy load.

Different context can have it mean different things. However, given the above, I think the single work most likely to represent it in a lot of cases would be trauma:

[Merriam-Webster]
1 a : an injury (such as a wound) to living tissue caused by an extrinsic agent
1 b : a disordered psychic or behavioral state resulting from severe mental or emotional stress or physical injury
1 c : an emotional upset
// the personal trauma of an executive who is not living up to his own expectations
— Karen W. Arenson

Baggage is something you have to carry around as an unwanted chore; it's not something that you look forward to dealing with.
Figuratively speaking, it would be uncommon for somebody to use the term emotional baggage to refer to something positive or happy. If they aren't talking about something emotionally scarring (traumatic), then they would normally either not use the term at all or they would qualify it in some way.
To paraphrase the example sentence slightly:

It reminded him of where he met his first love that didn't work out, and he had too much trauma from that experience.
Comment: "Emotional baggage is an everyday expression".  The *contributer* to Wikipedia wrote that has a nice sense of humour.


Give an example of a sequence of real numbers with subsequences converging to every real number

Question: Im unsure of an example
Give an example of a sequence of real numbers with subsequences converging to every real number
Answer: HINT: The rationals are a countable set, so they can be enumerated, and every real is the limit of a sequence of rationals.
Answer: It's a bit of work, but you may show that taking the sequence $$a_n = n \bmod{2\pi}$$ has a limit point at every point in the interval $[-\pi, \pi]$, where the endpoints points are never actually attained attained (otherwise $\pi$ would be rational).  So you may continuously map the interval $(-\pi,\pi)$ into $\mathbb{R}$ in you favorite way.  Take, for instance, the map $f: (-\pi,\pi) \to \mathbb{R}$ sending $x \mapsto \tan(x)$.  So now you have a sequence $a_n$ converging to every point $a \in (-\pi,\pi)$, then since tangent is continuous, $\tan(a_n) \to \tan(a)$, and $\tan$ is surjective onto $\mathbb{R}$, so you are done.
I realize that the first part, taking integers modulo $2\pi$ is not entirely necessary for the proof, since $\tan(x) = \tan(x + 2k\pi)$, but I think it's easier to break it into smaller problems.
Comment: Or based on the opposite idea, $a_n = f(n\pi\mod 1)$ where $f(x) = \frac1x\sin\left(\frac1x\right)$. The modulo operation is necessary in this case, though.
Comment: I think what you're referring to when you say $n\pi \bmod{1}$ is actually $n \pi - \lfloor n\pi \rfloor$ (the "floor" function).  The way you have written is not well defined.  i.e. $f(x)$ must be equal to $f(x + k)$ for any $k \in \mathbb{N}$, however $f(1) \neq f(2)$.
Answer: A related question that you can try:
Let $(a_k)_{k\in\mathbb{N}}$ be a real sequence such that $\lim_k a_k=0$, and set $s_n=\sum_{k=1}^na_k$. Then the set of subsequential limits of the sequence $(s_n)_{n\in\mathbb{N}}$ is connected.


Why does steamed potatoes sometimes have a smooth, banana-like texture?

Question: Sometimes when I steam potatoes, they have a lovely dry, fluffy, crystaline texture. Other times, they're the complete opposite, looking dull with a texture like that of banana.
Comment: Do you always steam the same type of potato? If so, what kind is it?
Comment: Do you store your potatoes in a cold place? Microscopic ice crystals that form inside when potatoes get cold will help create steam during cooking, producing a fluffier texture.
Comment: Cold storage converts the starches to sugars, which can certainly impact the texture, but generally in a manner opposite what's stated above, and no ice crystals are involved.
Comment: @Ecnerwal against the back of a fridge ice crystals may well be involved. We tend to keep new potatoes in the fridge at least in warm weather, and the veg drawer doesn't always have room. In this case you could tell as only those which had been touching the element would lose texture.
Comment: @ESultanik yes, I store them in the fridge at approx 5C
Answer: Could it be you are not using the same type of potatoes all the time? Different varieties of potatoes do have very different textures. The ones with the brown, rough, dusty skins ("russet" I think they are called?) usually cook up with the fluffy, dry, almost "sparkly" flesh. The smoother skinned ones tend to have denser, waxier texture inside. The pink, smooth ones ("rose" or "early rose") seem to fit the description of "looking dull" inside when cooked.
Comment: Russet's a specific variety of potato.  As a whole, they're generally called 'starchy', 'mealy', 'floury' or 'baking' potatoes, and are your normal ones for baked potatoes, mashed potatoes and deep frying.  'waxy', 'boiling' or 'roasting' potatoes (eg, red bliss) are used for cases where you want them to hold up and not turn to mush (eg, soups and stews, etc.).  There's also a class that's between the two types of potatoes, like many of the more recent yellow/golden varieties (eg, yukon gold) that can be used either way if needed.
Comment: Yes. Russet is what they are called in the US. They are 'starchy' as opposed to 'waxy'.
Answer: You mentioned in the comments that you store your potatoes at close to freezing in your refrigerator.  When potatoes get cold, microscopic ice crystals can form inside that will help create steam during cooking, producing fluffy texture like what you describe.
I'll bet that the inconsistency in your potatoes is due to slight differences in temperature in your refrigerator (i.e., some areas of your refrigerator might be 5°C but others 0°C; refrigerators are rarely 100% consistent).  It could also be the case that your potatoes were stored at near- or below-freezing temperatures before you bought them.
The cold will also promote the starch in potatoes to convert into sugar, which can cause the potatoes to taste sweet and/or cause premature browning.  This effect and the textural changes may be desirable for certain recipes, e.g., french fries.  However, for most recipes you will want to use potatoes that have never been close to freezing temperatures.


Usecase for approve and allowance functions of ERC20 token

Question: Could you please enlighten me on how approve and allowance functions work using a usecase? I dont understand the underlying operations of these functions. Especially, when a token owner delegates the right to spend his token by other user: how the ownership sign-off works, is this be done automatically?
Comment: https://medium.com/ethex-market/erc20-approve-allow-explained-88d6de921ce9
Answer: The original use case from back 2016 is that back in a day, smart contracts had no way to interact to incoming token transfer. (This has been now fixed with ERC-777 token standard and send()).
For you to interact with a smart contract with an ERC-20 token

You need to approve() amount of tokens on a smart contract address
You call a smart function that then in a turn calls token.transferFrom() function to take over the tokens from you and do something with them

allowance() is simply a function to check what's the current approve() limit.
Comment: Thanks Mikko! This means, the contract that I approve would use my address to sign-off tokens which require signing-off using my private key right? Does the signing-off happen seamlessly?
Comment: After the `approve()` has been done the smart contract is free to use the tokens and one can consider "the posession of" tokens to be on the smart contract. `approve()` is the only transaction that depends on your private key. Smart contract can control the tokens until you cancel to `approve()` by setting it to zero.