What's the difference between a toggle switch, radio buttons and a tickbox? What's the best cases these patterns can be used?

Question: What's the best cases these patterns can be use?
Comment: One is for turning things off and on. One for selecting only one and the last for ticking multiple options. Not sure what can be said beyond that. Ideally they are used for those cases.
Comment: This question will be of interest to you: [Should a toggle button show its current state or the state to which it will change?](http://ux.stackexchange.com/questions/1318/should-a-toggle-button-show-its-current-state-or-the-state-to-which-it-will-chan).
Answer: Well, it kind of depends on which system you are.
There are mobile guidelines for Android, iOS and Windows.
iOS, for example, doesn't use regular checkboxes (they are not called tickbox btw) or radio buttons but only grouped lists of elements (scroll down to "table view") or switches.
But from what I've learned, you use all of those controls like this:

Radio Buttons

For mutually exclusive options, but not for binary choices

If there are too many options (on Windows the number is 8) use a drop-down instead

Checkboxes

For selecting a binary option or multiple options in a set
Should always be used with positive commands, not negative like "do not .."

Switches

Are also used for binary options, but usually those that activate/deactivate something, like you would expect from a switch in real life

It is a good user experience to immediately change the affected setting by the switch and not only after pressing "save" or returning to the previous screen.
Because we have this expectation for a switch in real life (for example we know light immediately turns on)
Comment: Exception: If you have a binary choice and you want to force the user to make a choice then you need to use radio buttons with no default selection. If you choose to use a checkbox then the user could accept the default value without making a choice. With the radio buttons you can pop up text saying "Please choose A or B".
Comment: I think you are missing my point. Your scenario is where the user must answer in the affirmative. That's not really a binary choice. That's a single forced acknowledgement. A binary choice is where the user can choose either True OR False. If you use a checkbox that defaults to False then you're not sure if the user is choosing false or if they just clicked past the choice. If you have a real binary choice where you want the user to choose one or the other, you need a radio button with no default selection because now you have 3 positions. True, False, or no answer.
Comment: @HackSlash Usually, you have error validation in the form in most cases and will block the user from continuing unless he checks that checkbox and mark it in red error color for them to see. This is very common with "[ ]  I agree to terms and conditions", where you cannot continue without it.
Answer: The toggle switch general use is to start or stop something. Like Wi-Fi or Bluetooth access. It has the analogy of a light switch.

The radio button is used in a group of several other radio buttons where only one at a time can be selected. When selecting one, all other are deselected.

The tick box (or check box) can be used in groups of several other tick boxes, but have no dependency with others. Selecting one doesn't affect any other tick box. Checked represents true, un-checked represent false.
Answer: Toggle - Despite their relative popularity (eg, Apple use them as a standard interface control) toggle switches have an inherent state-action ambiguity; that is, it is unclear whether the label ('on' for example) is the current state, or the action.
Radio button - let users select one option from two or more choices. Each option is represented by one radio button; a user can select only one radio button in a radio button group.
Checkbox - There are various ways to improve the usability of such switches, and one has to remember that these are both fairly popular and only require a few learning iterations before most users get it. But from a cognition perspective a checkbox is far easier (and faster) to interpret compared to a toggle switch.
--------------------- Toggle example ---------------------

--------------------- Radio button example ---------------------

--------------------- Checkbox example ---------------------

At end if upto your context of utilising them, i.e., in what way you want them to be presented to user. For instance, toggle is default considered for on/off scenario but you could use it for camera selection with front or rear.
Reference URL -
Radio buttons or Toggle switch for one out of two options?
https://msdn.microsoft.com/en-us/library/windows/apps/hh465475.aspx
https://msdn.microsoft.com/en-us/library/windows/apps/hh700395.aspx
Toggle button vs. check box and toggle switch
Note - Do check above reference link for more clarity and understanding.
Answer: This selection control flowchart has suggestions on which control to use according to use cases. Might be a quick resource if decision trees are useful for you and your team.


Recording Tap Dance

Question: What mic would you use to record tap dance (specific which lavalier, what position)- I was thinking dpa 4061 at the heel, but maybe 4062x would be more suitable? or would you  rather use foley instead?
Comment: piezo the hardwood floor :D
Comment: A few questions... do you need to be that close? Are you going to be taping these to the dancer's shoes? Why not on a boom, are you going to be struggling with frame issues? [I'm afraid I can't answer your specific question on mic choice, the only DPA/B&K mics I own are the 4060 & 4006 - which do make for a very nice near/far combo.]
Comment: Hey Tetsujin, no I am going to use a KMR 81i & a Brauner as well. But I . want to have as many sounds as possible from the shoes as it is the most important part for this project to get a great tap sound. Would love to test (and probably have) a 4006 one day
Comment: @frcake I will do this from under the floor ;)
Answer: A wireless lav on the dancer and Foley replacement are only two possible solutions. And probably not even the most commonly used solutions. Conventional micing techniques, and barrier ("PZM") microphones are more commonly used than either wireless lav or Foley replacement.  Most of the details that are used to make these trade-off decisions are not disclosed in the question.
Comment: Thanks for the answer and sorry for the missing details. It will be a studio situation with a build wooden floor. I will have an additional KMR 81i & a Brauner mic. Either a contact mic or a d112 under the floor in a hole. I need the Tap sound for this project to be very rich in sound, so I want to have as many files as possible to choose from and wanted to check on the industry "standard". The dancer told me in live situation he is mostly miced with lavs, that's why I wanted to try it in the studio too.
Answer: check this out: midi shoes:
 midi shoes tapdj
or classic mic
pro 44 audio technica

Recording Tap Dance


Camping along ring road in Iceland

Question: I am planning on a circumnavigation of Iceland this summer and the Ring Road might be the only road available for lenghthy stretches.
I would like to know if camping along the Ring Road is permissable, especially once I get out into the more remote areas.
I would also like to know if ground/river water is safe to drink without purifying.
Comment: Useful: http://www.nat.is/camping/camping_sites.htm
Comment: I think this question is more on-topic on [The Great Outdoors](http://outdoors.stackexchange.com/) than here. I propose to migrate it.
Answer: Wild camping is permissible as long as you maintain a respectful distance from homes etc, but in some places it might difficult to find good spots to put up a tent close to the road. Based on my experience, the best spots are found taking side roads a little bit off the main ring road. Near populated areas you can usually find official camping sites (check the link provided by  MeNoTalk).
The water from small creeks/rivers is almost always safe to drink without purification as long as you avoid getting it downstream from habitations.
Answer: Along the Ring Road it's acutally harder to NOT find camping areas than to find one. They are literally all over the place. Prices and facilities can vary greatly. On some grounds you get free internet and hot showers are included as well. On other grounds (the more crowded ones like Skaftafell, the main camping ground at Vatnajökull) you even have to pay to recharge your cell phone.
But, they all offer toilets, which is why I wouldn't bother with wild camping if you stay near the Ring Road anyway. As for wild camping, it is allowed to some extend, as is explained here:

If you wish to camp on cultivated land or near residential buildings, fenced off farmland, or such, you have to ask permission from a landowner or other beneficiary before you pitch up the camping tent. The same rule goes if you intend to stay longer than one night.

If there is a camping ground nearby, you have to use one of those. I don't know what exactly is considered to be "nearby" though. For the sake of preserving the beautiful and very fragile landscape I strongly advise against wild camping in the more crowded areas.
Also, the camping grounds all have running water which is perfectly save to drink (even though it may smell funny). To save you from unneccesary trouble, I suggest you just stay at a camping ground.
Usually the price for one tent is around 8 ISK per night, Camper trailers are more expensive, but I don't know the price for those.
Comment: Had a brief look at camping.info, and the sole campground I've stayed on (at [Stafafell](http://www.stafafell.is/)) is not shown, so I can confirm the listing is incomplete.
Comment: *you cannot camp on land that is owned by someone without permission*, this contradicts [this answer here](https://travel.stackexchange.com/a/4094/2509), which sources the Visit Iceland website to state that, with some conditions, you do not need landowner permission for wild camping.
Comment: @gerrit: Thanks for your comment, I have worded the paragraph in question more clearly. Wild camping IS allowed, but not on cultivated land, etc. Plus, since there are camping grounds literally everywhere (especially in south iceland), I would never bother with wild camping anyway.
Comment: Right.  Cultivated land is very rare though; most of the land that is "in use" is used for sheep grazing.  The bit on fenced off land is more relevant.  When driving in summer in the south you're always close enough to a campground, but when cycling off-season, in particular in the east, one might not be, so it's still useful to know about wild camping.
Comment: @gerrit: Haven't thought about biking. Yes, it may be a problem to reach the next camping ground if you want to do something other than riding your bike during the day. You may want to have a look at [camping.info](https://en.camping.info/iceland/campsites), but I don't know if they really show ALL campingsites there.

Camping along ring road in Iceland


In an agile project is it ok to change the requirements of the sprint in the middle of the sprint?

Question: I have been in several projects before as a frontend developer when the requirements of the project change in the middle of the sprint. I want to be like "agile" and accommodating to change and flexbile, but I think this can be very hard on a front end developer and also extremely unfair because the front end developer is the last point in the process of developing a product because they are making things look right, and also connect it to the backend so the product will actually work. I think this is confusing for project leaders and customers, because often seemingly large changes are actually the most easy changes to get done, but then the seemingly minor ones takes days if not weeks to implement fully. Anyway because of the nature of agile projects and also the reality of working as a front end developer. I am wondering. Is it ok and normal for a project to make changes in the middle of the sprint and expect the same deadlines?
Comment: I don't know why someone downvoted this - it's a legit question in my opinion.
Answer: The Scrum Guide says:

During the Sprint:
No changes are made that would endanger the Sprint Goal
Quality goals do not decrease
Scope may be clarified and re-negotiated between the Product Owner and Development Team as more is learned

What this is saying is that reasonable changes may be made. If excessive changes are introduced then it is up to the Product Owner to decide if the sprint should continue or be ended early.
It is worth noting that excessive changes mid-sprint have a number of disadvantages including:

They make forecasting difficult
They can introduce waste as a result of the team having to re-plan
They may create confusion and reduce transparency

Comment: Thanks for pulling the Scrum Guide verbiage on this. If you'll excuse me tacking on, I wanted to highlight the word "re-negotiate". That seems to be forgotten too many times.
Answer: I realize that the answer below may not have directly answered your question. I'm going to leave it because, well, I'm a dummy, and there's no sense in hiding that.
The answer is, "Yes, requirements can change in the middle of a sprint, and they frequently will."
In the industry in which I currently work, requirements often change mid-sprint due to natural disasters, regulatory changes, vendor changes, system outages, and all sorts of weird goings-on. These things are outside your control (external factors) and you cannot predict when they will occur. But you have to handle them as they arise.
The requirements will change, tasks will be deprioritized in favor of other tasks and your sprint and product backlogs will change. This is where Agile beats the pants off of Waterfall.
Yes, your developers will pull their hair out. So will you. But you'll save money on haircuts.

Agile expects constantly changing requirements.
However, having said that, the team leadership can push back against the customer and make it clear that some of their expectations are unreasonable.
At the start of the sprint, the expectations were clear, and the team presumably negotiated with the customer for a fixed set of deliverables. Barring an extraordinary set of circumstances (natural disaster, regulatory changes, legal obligations, etc.), they committed to those deliverables and anything else should go into a future sprint.
Talk to the customer. Negotiate. Communication is key. In a worst case scenario, and they insist on the new functionality, they'll have to move other items on the sprint backlog into a future sprint to make room for the desired features. It's all about priorities at that point.
With any luck, you'll have a retrospective, and you can include this as a pain point and learn from it.
Comment: I think that is well said ... I will also just add. While I understand agile, and I think it is superior to waterfall no issues there. I think this philosophy can be abused, and it really comes down on front end developers hard. Because basically as a project leader it can be a license to not have a plan and whimisically order stuff. And as mentioned the front end developer is the last point in product development, so it hits them hard when deadlines have to be reached. It can be really unfair for them.
Comment: Another aspect is that today the front end of websites can be build extremely quickly and to a high standard. But that really depends on the overall planning of the project. The reason for this is the modern component architecture of javascript frameworks. If a developer has like a perfect idea of what he/she will do over the next few weeks, they can leverage the power of these frameworks and deliver great products built with great code. If there is disorganisation, I would say the length of time can increase several times due to the difficulty of reusing code and maintaining  good structure.
Answer: To me that's one of the many points in Scrum where it's more about instinct and balance than about rules. On the one hand the customer value is important and you don't want to waste time following a wrong path. On the other hand one want to shield the team from distractions and disturbance. So I'd have a look at four factors:

Is this an exception or is this happening every sprint? If this is common, your Scrum Master should have a long talk with your Product Owner.
Are we talking about small change requests? Or are we talking about changing acceptance critereas? A big change will alter the goal of a user story and thus should result in a new user story. My two cents.
Is there a policy in your organisation how change requests should be handled?
And finally: in my experience it depends a lot on the length of your sprints. Are we talking about two weeks each? Then maybe ask your Product Owner to write a new user story. Are we talking about eight weeks? Then small changes should be acceptable. But again, for me this is a lot about tact. Talk with the team, your Scrum Master and/or your Product Owner if you feel uncomfortable.


Swinging of a blade

Question: Hello,
does anyone here know how to simulate a long swinging of a blade? You know that high pitched sound you get when you have hit a metal. It does not seem to be a simple sinus tone. There seems to be some kind of modulation going on.
Thanks!
Answer: It sounds like you're looking for the metal ring off of the sword after it is unsheathed. It's usually performed as foley, but can be sweetened with some library effects.
Basically you'll need two pieces of metal, the first is long and dense enough to give you the length and heft of the scrape you're looking for. The second is smaller in order to achieve that higher frequency. You want something that is easy to handle, yet large enough to ring loud and long.
Check out this video on Gary Becker. At around :30, and again @ 3:10 he performs exactly the sound I think you're looking for.
You'll see that he has an actual sword, this contributes to the length and heft of the scrape (an actual sword isn't necessary, I've used wrought iron, angle iron, scrap metal,  etc. again you want about 1m long and dense). And a kitchen spatula, (small, light, highly resonant) that he scrapes along the sword's edge and points towards the mic.
Try short aggressive scrapes, long fluid scrapes, whatever is appropriate. You can then wave the spatula around to modulate the ring according to picture.
Hope that helps.
Comment: Thanks very much! Excellent advise and good video. Still to make it sing for a couple of seconds, foley may not be enough.
Comment: True, if you're looking for a couple seconds I really like Tim's suggestion of the Tibetan bowls/bells. That should offer you tons of sustain.
Answer: For THE WARRIORS WAY I mostly used a Tibetan singing bowl and a pair of those small Tibetan Timsha bells - the latter are very interesting as you can set up beating between the two bells and they are easy to move and perform dopplers, which is far more complex and controllable in the real world than via plugins....
See this video for how you excite/create continuous tones from a singing bowl:
http://www.youtube.com/watch?v=Bpw53tN6h8E
& the pair of Timsha Bells:
http://www.youtube.com/watch?v=1UDdyG7iB4o
Also worth trying spectral based time expansion with these as the beating is hypnotic when the rhythm is slowed down but pitch remains the same....
We also got some spring steel swords from WETA and suspended them on string & hit them - they resonated like crazy but the dopplers from them was very useful too
Comment: That is very interesting. That way you can actually control the length of the singing. Don't have Tibetan singing bowls though :-). But now that you mention it I can remember someone creating a similar singing sound by stimulating a half full wine glas in a pub years ago. Maybe that is the solution.
Answer: Do you mean the swish or the actual clang? For the clang after a hit you might try a fast vibrato that slows down? not sure without knowing which part you're talking about.
Comment: I mean the singing, when you pull a sword out of the sheath it sings on at a high frequency. Unfortunately real blades only seem to do that for a small moment. I just saw the Hobbit and there is one scene where an Ork pulls out his sword and raises it into the air and it sings beautifully for a long time. I am pretty sure they must have done this artificially. And now I am about to sound design something similar and I cannot make it sing.
Answer: The best luck I've had for the high pitched sing is to hit a metal putty knife with a screwdriver, then cut out the attack and fade in.  As for the modulation, a slow tremolo that shifts frequency and not volume could work for you.
Answer: Another idea...  I've used a baking sheet to achieve the unsheathing, singing blade effect.  Pull it off of a counter, dragging it down across the 90 degree edge of the counter top.  Do various takes at different intensities, with your hands positioned differently, and, depending on the baking sheet itself, with some practice you can actually get that thing to sing for you.  If nothing else, you'll have a great source to start with that you could then begin processing.
Comment: Thanks, will try that too and see what kind of sounds it produces.
Answer: Ok, so the singing part. If you have a knife block, you can get part of the unsheathing sound by pulling out of that if performed correctly. Layer that with a butcher knife along the back of something like a baking sheet mentioned above. You can try pots and pans, but thicker pots and pans will not resonate and you will not get a long sing. Don't forget you can compress the sing to hell to get some sustain out of it.

Swinging of a blade


Are there mathematical concepts that exist in dimension $4$, but not in dimension $3$?

Question: Are there mathematical concepts that exist in the fourth dimension, but not in the third dimension? Of course, mathematical concepts include geometrical concepts, but I don't mean to say geometrical concept exclusively. I am not a mathematician and I am more of a layman, so it would be appreciated if you could tell what the concepts are in your answer so that a layman can understand.
Comment: What about quaternions?
Comment: Not sure how to explain it in layman's terms, but the regular [octaplex](https://en.wikipedia.org/wiki/24-cell) is totally unique to 4 dimensions.
Comment: @MarcvanLeeuwen Indeed, it appears the OP is asking about concepts that exist _in four dimensions_ but not in three dimensions.
Comment: I've asked a similar question, these answers might be relevant: https://math.stackexchange.com/questions/374685/are-there-new-possibilities-in-higher-dimensions
There's also a book Things to Make and Do in the Fourth Dimension by Matt Parker.
Comment: This is a bit of nitpicking aimed against popular language, but there is no such thing as the (third or) fourth dimension. There is just _one_ (notion of) dimension (which notion applies to certain mathematical situations) whose value is a (usually natural) number; so that value, _the_ dimension, might be $4$.
Comment: Did you really mean concepts? (then no).
Comment: A related MO-Q https://mathoverflow.net/questions/47569/what-makes-four-dimensions-special#comment942403_47569
Answer: The one that sticks out for me the most is that there are five regular polytopes (called Platonic solids) in $3$ dimensions, and they all have analogues in $4$ dimensions, but there is another regular polytope in $4$ dimensions: the 24 cell.
The kicker is that in dimensions higher than $4$... there are only three regular polytopes!

Another thing that can happen in $4$ dimensional space but not $3$ is that you can have two planes which only intersect at the origin (and nowhere else.) In $3$ dimensions you'd get at least a line in the intersection.

I don't know if this also counts, but linear transformations in $3$-dimensions always scale one direction (that is, they have a real eigenvector).  This means that in all cases, a line in one direction must either stay put or be reversed to lie upon itself.  In $4$ dimensions, it's possible to have transformations (even nonsingular ones) that don't have any real eigenvectors, so all lines get shifted.

Also not sure if this counts, but there are no $3$ dimensional asociative algebras over $\mathbb R$ which allow division (they're called division algebras) but there is a unique $4$ dimensional one. (Look up the Frobenius theorem
Comment: I would think that the third point doesn't count: surely it's just about the parity of the dimension, because an odd order polynomial must have a real root but even order polynomials can be constructed as products of quadratics which are irreducible over the reals?
Comment: @PeterTaylor well, the question did not specify "special to $4$", it said "exists in $4$ but not $3$" so that doesn't seem to be an issue. The thing I thought that might be objectionable is that the property is negative ("in $4$ dimensions there are transformations that don't...")
Comment: @Yakk I don't have any problem stretching by a factor of $1$. But anyhow, I switched it to scale to make it slightly better.
Comment: "stretch one direction" -- some kind of clarification that eigenvalues of 1 don't "stretch" might be useful.  Not sure how to not make it awkward.
Answer: The fourth dimension is, in some ways, very peculiar.
The $3$-dimensional Euclidean space has a unique differentiable structure. In fact, the same is true in any dimension not equal to $4$. By contrast, the $4$-dimensional space has a continuum of incompatible differentiable structures. Intuitively, this means that something that looks like the familiar $4$-dimensional space can have a large variety of rather odd geometries.
An at most $3$-dimensional sphere admits a unique differentiable structure (there are no exotic spheres).
It is not known whether there are exotic $4$-dimensional spheres, or whether there are finitely many of them (in contrast, in any other dimension, there are only finitely many differentiable structures on the sphere --- e.g. $28$ in $7$ dimensions).
Comment: $28=4\cdot7$ by coincidence?
Comment: Very weird indeed!
Comment: For example a symplectic structure (https://en.wikipedia.org/wiki/Symplectic_vector_space). See in a much larger perspective https://www.math.tecnico.ulisboa.pt/~xvi-iwgp/talks/ACannas.pdf
Answer: Double rotation. In 4 dimensions we can have 2 rotations independent of each other:
$$ \begin{pmatrix}
 \cos\alpha & \sin\alpha & \cr
-\sin\alpha & \cos\alpha & \cr
&&  \cos\theta & \sin\theta & \cr
&& -\sin\theta & \cos\theta & \cr
\end{pmatrix}. $$
Comment: This is closely related to the thing about 2 planes intersecting at a point, mentioned in rschwieb's answer.
Answer: The fact that $\mathbb{R}^4$ can be given a multiplication such that with vector's addition, it has a structure of (non commutative) field, i.e., quaternions. See remark 1  below.
Whereas one can prove that it is impossible for $\mathbb{R}^3$ to have a vector multiplication such that, with usual addition of vectors,  $\mathbb{R}^3$ is a field.
I just saw now that at the end of his answer @rschwieb has mentionned "division algebras" which in fact is equivalent to (non commutative) or "skew") field (thanks to Tomasz for having done this remark).
Remark 1 : For quaternions, see my answer to what is the relation between quaternions and imaginary numbers?
Remark 2 : Think for example to an unsuccessful candidate, cross product, which is

not associative : in general $(\vec{u} \times \vec{v}) \times \vec{w} \neq \vec{u} \times (\vec{v} \times \vec{w}).$
does not possess a neutral element : no vector $\vec{u_0}$ exists such that for all $\vec{v}, \vec{v} \times \vec{u_0}=\vec{v}.$
Comment: A non-commutative field is the same as a division ring. A division ring with a compatible vector space structure is the same as a division algera.
Comment: Could someone edit this answer to be understandable by a layman like what OP identifies as?
Comment: user1717828  see the reference I just introduced in my answer. Quaternions can be understood as an extension of complex numbers under the form $r+iV$, where $r$ is a real and $V$ an 3D vector, with a rule of addition which is $(r+iV)+(r'+iV')=(r+r')+i(V+V')$ and a rule of multiplication reminding the product of complex numbers $(r+iV)(r'+iV')=(rr'-V.V'+i(rV'+r'V+V \times V')$
Comment: [Here](https://math.stackexchange.com/a/865139/11619) I give a simple proof that 3-dimensional real division algebras don't exist.
Comment: Tessarines are a commutative 4D ring.
Answer: At the risk of sounding flippant, I'm going to propose the universe as one such example.  It is a peculiar, but experimentally well verified fact, that the universe has four dimensions (three spatial and one of time).  To the extent that the universe is described by mathematical laws, it is an example of something that exists in four, but not three, dimensions.
You may ask: What is the mathematical explanation for this peculiar fact?  Many physicists have asked themselves the same question.  Some answers have been proposed, none of which are yet considered the final word:

The most scientifically "modest" proposal is that it has to do with "running of coupling constants under renormalization".  In layman's terms, the idea here is that in dimensions other than four, the fundamental fields that make up the universe are strongly coupled, so that it becomes impossible for simple objects like atoms to exist.  Without atoms, there is no life, and thus such a universe cannot have people in it to ask the question "why does my universe have this many dimensions?"  (This is called an "anthropic argument", and has a number of criticisms, some mentioned in the linked article.)
Other anthropic arguments come from general relativity, which suggests that the universe may be unstable or inhospitable for life in various ways if it had higher or lower dimension.
String theory predicts that the universe is part of a bigger multiverse that has (depending on the flavor of string theory) something like, ten, eleven, or twenty-six dimensions.  Most of these dimensions get curled up so that they become very small (this is called "compactification").  Some physicists have gone looking for extra spatial dimensions, but all such searches have turned up empty so far.
Some people speculate that the reason why the universe is 4D has to do with the peculiar topological properties of four dimensional space.  As far as I know, no one has a concrete proposal for how this should work--just the aesthetic observation that four dimensions seems to be special in many ways (e.g. exotic spheres and exotic $\mathbb{R}^4$, not that these in themselves explain anything).

Of course, no one has totally ruled out the possibility that there are other universes with different numbers of dimensions, but given that four dimensions seems very stable in our experience, it is interesting to ask whether this is mathematically required.
Comment: Comments are not for extended discussion; this conversation has been [moved to chat](https://chat.stackexchange.com/rooms/98412/discussion-on-answer-by-yly-are-there-mathematical-concepts-that-exist-in-dimens).
Answer: If it counts: The $4$-dimensional unit sphere $S^4$ in $\mathbb R^5$ has the biggest volume of all unit spheres.
Comment: NB to people who didn't notice. This is 5-dimensional space, not 4. But the 3-sphere in 4d space also has a bigger volume than the normal, 3d sphere
Comment: I would argue that the sphere is a perfect example of what is *not* new to four dimensions because it is a straight foward generalization of what we have in two and three dimensions.
Answer: You have neat non-orientable surfaces which embed in $\mathbb R^4$ that do not embed in $\mathbb R^3$, such as the Klein bottle and the real projective plane.  For instance, see: A non orientable closed surface cannot be embedded into $\mathbb{R}^3$ or this MathOverflow question on the Klein bottle.
In other words, you have these interesting homogeneous closed surfaces on which there's no consistent way to define counter/clockwise in $\mathbb R^4$, but you can't actually construct them in the 3-d space we live in.
Note: in $\mathbb R^3$, you can embed the non-orientable Mobius strip, but the Mobius strip is a bit different as it is a surface with boundary so is not homogeneous.  You can think of the Mobius strip as a slice of a Klein bottle or the real projective plane.
Comment: Right. I personally don't find that a very remarkable property about $\mathbb{R}^4$ though – it's merely that it's "big enough", allowing enough movement for embedding such manifolds. The manifolds themselves are only 2-dimensional.
Comment: @leftaroundabout Well, I think the interesting thing is that these surfaces don't embed into $\mathbb R^3$.  Yes, the properties of the manifolds are simply 2-d properties, but if you restrict to $n$-dim Euclidean spaces (I expect the OP was thinking about Euclidean spaces), the question of what types of submanifolds you have is interesting.
Comment: I would guess that there are non-orientable n-manifolds that can be embedded in R(n+2) but not R(n+1), for any n≥2.
Answer: If you look at real algebras (roughly speaking: arithmetic over vectors of real numbers), there is a 4-dimensional real division algebra, but no 3 dimensional real division algebra.  This means that you can construct a 4-dimensional definition for addition, subtraction, multiplication, and division which follows the rules we intuitively expect those operations to follow, but you actually can't do it in 3 dimensions.  If you try, you run into inconsistencies with how you and I normally think division should behave.
Real division algebras exist in 1 dimension (real numbers), 2 dimensions (complex numbers), 4 dimensions (quaternions), 8 dimensions (octonions), and 16,32,64... dimensions (sedions).  You can go look up rules for how to construct a meaningful concept of division in each of them.  The sedions are considered to be mostly just a mathematical peculiarity -- its really hard to find real life applications of them.  Octonions are really hard to use in real life (there's an effort to make a grand unified theory(GUT) with them in physics, though its not the most popular GUT candidate).
As for the others, you can use them all the time.  Obviously you know the real numbers.  Complex numbers get used in all sorts of situations in higher math for many reasons (one is that they're analytic.  Another is that they model signals that real life engineers are interested in).  Quaternions get used all the time to model rotations.
And that's all of them.  There simply isn't a 3-d real division algebra.  Its proven that one cannot exist.
Answer: Things that are completely new to four dimensions, that is, they appear first in four dimensions, but not in one/two/three dimensions, and which are also not straight forwards generalizations of concepts in one/two/three dimensions:

Double rotation (a way to rotate in two independent way simultaneously)
duo-prisms and duo-cylinders (geometric objects that "visualize" the concept of double-rotation).
A centrally symmetric self-dual polytope other than a polygon (24-cell, which is even regular),
More than one way to develope differential geometry on a manifold (e.g. multiple differentiable structures on $\Bbb R^4$ and maybe the 4-sphere)
Polytopes that cannot have rational vertex-coordinates, or polytopes which have strange realization spaces (not connected or not simply-connected, ...). For example, there is a (combinatial type of) polytope that can be realized in two ways, but these two ways cannot be continuously deformed into each other without changing the combinatorial structure of the polytope at some point.
Polytopes in which there is an edge between any pair of vertices, other than a simplex (so-called neighborly polytopes).
A knotted surface, e.g. a sphere embedded into 4-space, in such a way that it is free of self-intersections, but cannot be continuously transformed into the "standard embedding" without creating self-intersections in the process (okay, this is kind of a straight foward generalization of knots from 3D).
Answer: It doesn't properly answer the question but maybe it is worth noticing : James-Stein estimator.
For Gaussian vectors in dimension $m\ge3$, the estimator
$$
\hat\theta_{\rm J.-S.} = \left(1-\frac{(m-2)\sigma^2}{\|\bar X_n\|_2^2}\right)\bar X_n
$$
 is uniformly better than the empirical mean $\bar X_n$ with respect to the Mean Squared Error measure $\mathbb{E}\left[\|\hat\theta-\theta\|^2_2\right]$.
It consists in shrinking the vector.
Answer: My answer is a much more basic one, so much so that part of it is almost non-mathematical.
Three-dimensional space can be fully visualized by human beings. Four-dimensional space, however, can only be inferred by analogy, or describing analytically, usually by extending theorems in lower dimensions making them definitions in higher dimensions.
For example of the latter, by formula, think of the formula for distance in one, two, and three dimensions. In all three cases, we may regard the situation as being in 3D, where distance is found by the square root of the sum of the squares of the differences of coordinates. We can see that. In 4D, by contrast, we take what was a theorem such as distance in lower dimensions and simply make that the definition. Can you really SEE the distance of point (1,1,1,1) to the point (2,2,2,2), which happens to be 2? Can you take out a ruler to get at least approximate verification of this?
On the other hand, by analogy, think of visualizing a person moving out of just three dimensions and going into the fourth dimension. How do we visualize that? Think of you in three dimensions standing on a plane of two-dimensional entities. They see only line segments representing contact points made by your two feet. Now jump up. The segments shrink and disappear (not necessarily at same exact moment, depending on how you jump). The 2D dwellers may ask:
"Where did the 3D man go?" Well, you really did go off the x, y plane by using the z-direction, which 2D people can't visualize.
If there were a 4D man in Brooklyn, New York, by this analogy, and if he moved in the fourth dimension (whether spatial or temporal, doesn't matter), he - or rather his 3D "contact point shadow" - would seem to disappear from Brooklyn as he moved outside our limited view, and then suddenly appeared in, say, Tokyo.
P.S. Perhaps we can get the 4D man to fight Rodan or Godzilla while visiting Tokyo?
Answer: Going in the other direction, (nontrivial) knots exist in three dimensions, but not in four.
Comment: That's false. You just need to tie up a sphere instead of a circle.
Comment: @John, I'm defining a knot as a continuous image of a circle.


Entrance fee for Zion National Park: Paying for a car vs. paying per person

Question: Entrance fee per vehicle for Zion National Park is $30. But it is suggested/even mandatory to leave the car in Springdale and take the shuttle bus. As there are four of us, we would have to pay $15 per person to get in the park, instead of just $30. Am I missing something here?
Comment: Just a side note, its an amazing place!
Answer: So, according to the National Parks Service:

Weekly Passes
Weekly passes are non-transferable and are valid for 7 consecutive days including the date of purchase. Weekly passes may be upgraded to annual passes within 7 days of purchase.
Private Vehicle: $30. Valid for 7 days.
  Admits private, non-commercial vehicle (15 passenger capacity or less) and all occupants to Zion National Park, including both the Zion Canyon and Kolob Canyon areas.
Per Person: $15. Valid for 7 days.
  Admits one individual with no car to Zion National Park, including both the Zion Canyon and Kolob Canyon areas. Typically used for bicyclists, hikers and pedestrians. Youth 15 and under are admitted free.

So, no, you are correct in that for a car with 4 people, it would be considerably cheaper (half the price!) to take the car in. However:

Where To Park
Parking is limited inside Zion, and parking lots at the Zion Canyon Visitor Center commonly fill by mid-morning. To avoid parking hassles, park in the town of Springdale and ride the free town shuttle to the park. You can park anywhere along the road in town that does not have a parking restriction. To find the shuttle stops, look for the ''Shuttle Parking'' signs throughout town. If you are staying at a lodge or motel, simply leave your car there and take the shuttle to the park. Tune your radio to 1610 AM for additional information.
...
The Zion Canyon Scenic Drive will close to traffic once all legal parking spaces are full
...
Parking is usually full by 10 am

So you'd have to aim for an early start, and be prepared for some hastle if you try to move your car later in the day, if you want to take your car in to the park. Note that if you do take the car in to the park, it is still possible to use the shuttle bus to get around (during shuttle bus season). So those are your options.
Alternative
The "America The Beautiful" annual pass costs 80USD, lasts for a year, covers every national park, monument etc in the US, and gives entrance to:

A pass covers entrance, standard amenity fees and day use fees for a driver and all passengers in a personal vehicle at per vehicle fee areas (or up to four adults at sites that charge per person)

So if you were looking at paying $60 total for entry on foot, and think even one of you might visit another national park, monument, forest or grassland, then it would be well worth considering.
Comment: That is what I thought. However, I am considering the annual NP pass for the four of us, it looks like if you enter the park without a vehicle, the pass is still good for 4 people, which would save us money even if we got into only 2 national parks. (It is 80$)
Comment: @sara haha - I just edited a mention of that in while you were writing the comment. I think it might well be the best choice for you.
Answer: I have no source to prove this, but from several personal experiences, here is what you can do:

you enter by car and buy a pass for the car.
Turn right around and park outside
Use the shuttle to enter the park. Show the receipt and up to four people can get in on it.

That was also recommended by a ranger that we asked about it.
This is from the 2013 and 2015 summers, and things can always change.
As others mentioned, if you go see multiple parks, it is cheaper and easier to get the 80 $ annual pass. It is always good for four people, even in the shuttle. Note that two people can sign it and use it independently, also in a later vacation. I recommend you put only one signature on it right away, so you have the option of adding someone else later.
Comment: They never close the traffic to the_park_ itself, as it is a connection road through the park. The close just the _Zion Canyon Scenic Drive_ (which is a dead end that branches off the main road), _and_ all parking lots will be full. So after 10 am you can still enter the park, but then just drive straight through and out the other end. _And_ you might have a 60 minute wait time at the gate.
Comment: This is the kind of real experience I lacked. I did wonder if there was any leeway, but didn't want to suggest it.
Comment: @CMaster But in your answer you quote that they actually close the traffic once its full. Having a read, it seams you don't reach the pay station at all ?
Answer: As a Utah native who loves Zions, has lived in Southern Utah and well, generally treats that area as his backyard I can't help but answer this.
Answer: We are at the end of the summer season and school in Utah has already started, if your planning to go in the next couple weeks unless you are going on a Saturday, Sunday, or Labor Day, the parking lots aren't going to be crazy. So ignore the shuttle and take your own car in and save 30 bucks.

Now, there are 2 other parks in the area, I recommend getting the Annual pass as others have mentioned. Bryce Canyon is amazing. Then you should take the shuttle cause it's nice and relaxing after spending all day in the park.
As a note, if your not planning on hiking up on the rim on somewhere in Kolob canyon, then the bottom of Zions is considerably lower in elevation then the surrounding area and it can and will get over 100' F even late into September. Also Zions is subject to flash floods that close attractions like The Narrows or The Subway and these tend to happen in the afternoon. So you should think about getting an early start even if you aren't going on a weekend/holiday.
All that in mind, I've never had a problem parking at the visitor center if I got there by 7:30 - 8:00 am (even in the summer).
Finally as a bonus tip about 20 miles north of the Springdale/Zions turnoff on I-15 there is a short (3.5 - 4ish miles) beautiful, red rock hike to a waterfall that's $10 bucks (self pay, be honest, they use the money to clean the trail) and avoids all the congestion in Zions if that's your type of thing.
Comment: Quite perfect  +1.
Comment: @Fiksdal, it's suggested that you park in Springdale because during the height of the season parking late in the day is limited inside the Park. I was trying to illustrate the reality of the situation. I.E. as season wanes parking's not horrible, you can just drive in and pay for your car, or if you have any desire to see another park, get the pass. Or if your desire is to see X, here is a beautiful X that costs less, the locals recommend just outside the park.
Comment: @Fiksdal, Zions is a very hot very dry canyon park that is subject to flash floods. Due to the heat and tendency for flash flooding in the most popular hikes/waterfalls (which happen to be in slot canyons), locals and those who do their research know that the best time to be in the park is early in the morning. Hence why the parking lots fill up so quickly. Now the situation isn't as bad as it's made out to be but like many places that rely on tourism certain recommendations can and do take advantage of the unawares to wring extra money out of them. The shuttle one would be one of them. cont.
Comment: cont. In my post I try and lay out why you would want to start early (heat) that generally if you get there by X time you won't have an issue with parking any time of year, and that during this particular time of year parking isn't much of an issue any time of day, but heat still is. As parking is central to the price discussion (lack of parking is why they tell you to park in Springdale) I thought that sufficient to answer the question.
Comment: @Fiksdal Not could, but should, unless it's Sat, Sun, or Labor day.
Comment: @Fiksdal, how's that?
Comment: +1 -- this is the kind of thing you should start early in the morning _anyway_. Parking lot was only 1/2 full around 7 AM when I was there (late July 2016).


Salesforce Data Extensions not available for Contact Builder Data Model

Question: Why are data extensions in Salesforce Data Extension folder/sub-folder not available to be added in the contact builder data model? Is this a very specific design restriction? To the best of my understanding having data extensions in the Salesforce data extension folder only serves as a directory that can enable tracking to be sent back to Salesforce when sends are made through Email/Automation studio. Why is this folder not available when building contact builder data model? Am I missing something?
Thanks!
Comment: @garek007 - you are mixing Salesforce Data Extensions with Synchronised Data Extensions. The latter are indeed available in Contact Builder, but are not the ones mentioned in the original post.
Comment: @LukasLunow you are right, I must have misinterpreted what the OP was asking. my bad
Comment: In a sense, they are available. Go to Synchronized Data Extensions under the Data Sources Tab and you should see them listed. They are already synced up. I'm not sure, but I imagine this is why they are you can't set up your own relationships with them. And I haven't tried it, but you should be able to link to these in an attribute group as well.
Answer: Salesforce Data Extensions are indeed not available in Contact Builder - only in Email Studio. This is a limitation of the application, you are not missing anything. I normally set up the entire contact model in Data Designer using regular data extensions, and only use the Salesforce Data Extensions for e.g. Guided Sends. Remember, the contact model is mainly utilised in Journey Builder, which always will push tracking back to Sales Cloud, regardless what type of Data Extension is being used as entry event.
Comment: thanks @lukas! That is what I thought as well, but wanted to check. The ask here was to simply use a certain segment which is already part of Contact Builder Data Model for certain (adhoc) sends. I think the same can be achieved using a DE populated with a query or (may be) a filtered DE.


Why? Did Allah choose Isa(Jesus)(as) out of all the other prophets to be born a miracle? And choose him to come back before day of judgment?

Question: I usually have debates with my mum who is a hard core Christian and every time I tell her that Muhammad(pbuh) is the best of all creation she tells me 'then why did god choose Jesus(as) out of all the prophet to be born a miracle and choose him to come back at the end of times?'.
Comment: This is a logical fallacy. She could as well ask "Why did God choose you to be her son out of 7 billion people?". Miracles are given by Allah, and we don't question them. Being born without father does not imply _betterness_ of one (Jesus pbuh) over the other (Muhammad pbuh). Same for coming back at the end of times. Those are miracles given by the Creator, not of the creation's achievement. So one should look at the source and give credit where it's due.
Comment: Although I don't know the answer to this, it still makes more sense to send Jesus (A.S.) back to earth instead of any other prophet, given that Christianity is the most corrupt of the 3 Abrahamic religions. This could be one of the reasons. But Allah knows best.
Comment: Here are some thoughts, in case you find them useful. Note that God constantly referred to the Jews as "stiff-necked", that is, rebellious. And he sent many, many prophets that the Jews rarely listened to. Perhaps the miraculous birth of Jesus was a more vigorous means of getting them to listen? As for Jesus being highly honored, perhaps it is for similar reasons: perhaps God is doing it in order to make the point that the Jews should have listened to a guy who was born miraculously.
Answer: This question is like asking why did Allah create Adam before Muhammad s.a.w: This is because He is the creator and He does whatever He wills.
Comment: Salam and Welcome on Islam SE. Please consider taking your time and take our [tour] visit our [help] to learn more about the site and model. We are not an internet forum therefore this is not an answer as we expect here, so please read [answer] to learn what we expect here for good answers. I think almost all of us agree that Allah knows best! But we are asked to use our mind ...
Answer: Allah used to send prophet and gave them miracles according to the need of time. Hazrat Muhammad (PBUH) was sent at the time when the Arabs were too much interested in poetry and the best poet's work was hanged at Kaaba. So our Holy Prophet was give the Quran and despite many challenges the non-believers failed to produce any surah like the smallest one in Quran. Hazrat Musa (Alaih-Salam) was given the miracle of Hand and wooden log as this was the time of witchcraft. Hazrat Isa'(Alaih-Salam) was born at the time when there was prevalent the eastern medical knowledge (So-called TIB). This is my humble opinion and real knowledge is with the Almighty.
Answer: When you consider the many prophets who were slain by the jews and their general attitude towards prophets, the lack of respect and constant challenges directed at them , ie. Accusations thst they are just magicians soothsayers and the consistently obstinate nature of the jews, especially the levites and leadership amongst them( pharisees, saducees :sanhedrin). It seems God decided to send a prophet who they would have to take seriously, as a baby who can speak, born of 1 of the, if not 'The' most, noblest of families aswell as being extremely pious and being of a pure and innocent character and disposition. You could not simply call this child a magician, who is obviously from amongst your own, and from the best at that, whose cousin Yahya( john the baptist) PBUH was a prophet and if the jews did not believe that they certainly knew and know him and his father Zechariah (PBUH who was also a prophet) as being very pious and righteous persons. This was in effect Gods final message as well as warning, the severity of which is blatantly outlined by God sending a prophet whose credentials can in no way be doubted, affirmed by yahya, zechariah and the pious and temple servant maryam(mary) his mother.
The 2nd reason i believe is that after coming back from babylonian exile, brought back by cyrus. The jews established a law that was and still is 1 of the most baffling and revolutionary jewish laws ever, going against the god given methods for recording ones ancestry and genealogy. The jews from the persian period onwards declared that you were a jew, ie.you could inherit your righteous jewish soul, as long as your mother is a jew, regardless of who your father is. So it was now matrilineal not patrilineal n in israel today if your father is a jew but not your mother your not considered jew, and are a 2nd tier or class jew! So when jesus was born to mary who is from the davidic line, which is the main pre-requisite to be acknowledged as the messiah, and born to Only a woman, a pious woman from noble davidic stock, it was as if God was testing them! It was a means for the jews to control the membership of who can join their special israelite family, as daughters and who they marry are far essier to control than controlling your sons and who they marry and who they simply have extra marital relations with that more oft than not result in children who are now technically israelites, just like the Samaritans who were of this category of jews.
So it was God probably saying "ok, you changed the law, then lets see how you like your messiah who has not jewish father only a jewish mother who by your law carries the collective spirit of israel". The jews made more laws like for the levites and their kohanims or cohen, ie. Priests from the tribe of levi, to be considered a righteous cohen both your parents must be jews, however the messiah doesnt fit in that law as he would not be from the tribe of levi but the tribe of david.
Hope that helps, salam
Answer: All Praise to Allah Subhanahu wa Taala and blessings of Him be on Prophet Muhammad peace be upon him His family and companions
Indeed Prophets show different Miracles as a sign for those who could understand, This beautiful Hadith shows that Every Prophets are Higher in Status and as you stated Prophet Muhammad peace be upon him is not only the best of all  creation but also the most beloved of Allah Swt,

Narrated Ibn 'Abbas: that a group of people from the Companions of the
  Messenger of Allah (ﷺ) sat waiting for him. He said: "Then he came
  out, such that when he came close to them, he heard them talking, and
  he heard what they were saying. So some of them said: 'It's amazing
  that Allah, the Mighty and Sublime, has taken a Khalil (close friend)
  from His creation. He took Ibrahim as a Khalil.' And some of them
  said: 'That is not more amazing than speaking to Musa, He spoke to him
  with real speech.' And some said: 'And 'Eisa is the word of Allah and
  His Spirit.' And some said: 'Adam was chosen by Allah.' So he (ﷺ) came
  out upon them and said his Salam, and said: 'I have heard your words,
  and your amazement that Ibrahim is the Khalil of Allah, and he is
  such, and that Musa is the one spoken to by Allah, and he is such, and
  that 'Eisa is the spirit of Allah and His Word, and he is such, and
  that Adam was chosen by Allah, and he is such. Indeed I am the beloved
  of Allah and I am not boasting, and I am the carrier of the Banner of
  Praise on the Day of Judgement, and I am not boasting. And I am the
  first intercessor, and the first to have intercession accepted from
  him on the Day of Judgement, and I am not boasting. And I am the first
  to shake the rings of Paradise (meaning on the gates of Paradise) and
  so Allah will open it for me and admit me into it. And with me will be
  the poor people from the believers, and I am not boasting. And I am
  the most noble among the first ones and the last ones, and I am not
  boasting."(Tirmidhi)

And Allah Swt says in Quran

وَإِنَّهُ لَعِلْمٌ لِّلسَّاعَةِ فَلَا تَمْتَرُنَّ بِهَا وَاتَّبِعُونِ
  ۚ هَـٰذَا صِرَاطٌ مُّسْتَقِيمٌ
And indeed Eisa is a sign* of the Last Day, therefore do not ever
  doubt in the Last Day, and obey Me**; this is the Straight Path. (*
  The advent of Prophet Eisa to earth for the second time. ** By obeying
  the Noble Messenger.)(Quran 43:61)

Prophet Isa peace be upon him is one of the sign of the End of times.He will come back in the end of times and how amazing it is that he would come as an Ummati of beloved Prophet peace be upon him,he will follow Shariah of Prophet Muhammad peace be upon him and spread his teachings.
There is a narration and it is said that Prophet Isa peace be upon him wished to become ummati of prophet Muhammad peace be upon him after one incident which is mentioned in Nuzhat ul majalis.

Once Prophet Isa peace be upon him passed by a luminous mountain that
  was sparkling with light. He said to Allah 'O Allah! Bless this
  mountain with the power to speak.The mountain spoke and said, 'O
  RoohAllah What do you desire?' He replied, Tell me your state.' The
  mountain said, A person lives inside me.Prophet Isa peace be upon him
  said to Allah,Allow me to see him,The mountain split open and a very
  handsome  pious man emerged from it. This pious man said, I am the
  follower of prophet Musa peace be upon him. I supplicated to Allah
  that He let me live until the time of His beloved Messenger SallAllahu
  Alaihi wa Sallam so that I may have the honour of seeing him and also
  be privileged of becoming his follower. Alhamdu-Lillah! I have been
  busy worshipping Allah inside this mountain for 600 years.Prophet Isa
  peace be upon him asked Allah, O Allah Is there anyone on this earth
  dearer to you than this person? Allah answered: 'O Isa! Whoever from
  the Ummah of Muhammad fasts for a single day in the month of Rajab, is
  dearer to me than this person.' [Nuzha-tul-Majaalis, Vol. 1, Page 155]

Allah Swt and His Messenger knows best.
Comment: This does not answer the question, rather merely reiterates the fact mentioned in the OP :'(


FCPX Crashes again and again

Question: I was working on a project in FCPX. Suddenly it crashed. After that the library on which I was working is not opening.
Whenever I try to open it it crashes again. It was my 2 weeks of edit. How can I recover that lease help me ?? The error message I get is attached.
Comment: If you could file a bug report with Apple at [http://www.apple.com/feedback/finalcutpro.html](http://www.apple.com/feedback/finalcutpro.html) and include the crash log you have above, I'm sure they'd appreciate it.
Answer: Hold down the option key while you open Final Cut in the Finder.  This will open a dialogue which asks you to select a library.  DO NOT select a library from the list.  Instead, click the "new" button, name it "blank_Library" or something, select a destination, and click "OK".  This process should start Final Cut cleanly.  If FCPX has crashed at this point, then your problem is with the application itself, and you need to re-install.  If everything's OK at this point, you might have a corrupt library.
Assuming that FCPX is running, now you'll want to try to open the project upon which you're currently working.  Go to File->Open Library.  You should see the library which contains your project in the list.  Click it.  If FCPX crashes on this step, you know there's a problem with the current library.  If it doesn't crash, it could have been another open library which was corrupt and causing your crash.  If everything works at this point, carry on with your day.  If not, proceed to the next step.
Option-double-click to start FCPX again.  From the dialogue, select the blank library that you created in the first step. Click "OK".  Quit Final Cut.  This will ensure that the next time you try to open the program, it won't try to open the corrupt library.  Next, Spotlight search "Final Cut Backups".  This folder contains backups of all of your projects.  If the library which contained your project was called "Skateboarding_Kids", you'll see a folder called "Skateboarding_Kids".  Open that.  Within, is an iterative list of backups sorted by date.  Open the most recent one.  Did Final Cut crash?  If not, carry on with your day.  If so, repeat the steps in this paragraph, but open the next-oldest-to-the-last-backup-you-just-opened.
If none of this works, then my guess is that you're running a NAS or a SAN, and it's a network problem that's causing the crash, but I don't know enough about your system to say.
Hope this helps.
Comment: I tried to hold down the option key while starting Final Cut Pro but no dialogue came up asking me to select a library.
Comment: really?  works for me.  how are you launching final cut?  Try holding option while double-clicking the icon in your applications folder.

FCPX Crashes again and again


Making something not look clickable

Question: I haven't tested this theory, but I have a feeling users of my website may believe that the 'Concept' tag is clickable, when it isn't. How can I make it clear that this is not a button?
Comment: What is the larger context, and the purpose of this tag?
Comment: I've put up a quick suggestion based on the info you've provided. Will there be more than one tag displayed in this area, or just the 'concept' tag?
Answer: We don't have the larger context of your problem, so here's some quick thoughts:
You could try making an element that looks more like a banner (or a bookmark). If you want to reduce the visual noise, you can make it a bit more subtle, so the other content stands out. You can use a lighter font so it's distinct from the actual content.

Here's a version w/ lighter and tucked completely into the corner, and one where you don't put any borders, just a simple gray text.
Comment: These are great options. I recommend number 1, as it is the most obvious, and does not looks like a button or a link.
Answer: There's two ways that I think tags are typically different from buttons:

They have less padding
The colours and text aren't designed to stand out so much, i.e. washed out background colour and less contrast between background and foreground colours

GMail:

UX.SE:
Answer: Here's another way to think of the issue, that comes in two steps:

what do people think should happen when they click on [Concept]?
can you implement that?

If people click it, most likely they're hoping to sort of "zoom in", to somehow get more details about the tag content.  So maybe you can show a list of everything that's tagged with "Concept".  But if all you can do is show a little pop-up defining what a "Concept" is, that's still granting the user some extra detail.

Making something not look clickable


Which part of oranges contain fiber?

Question: I think it's pith, but here (non-english country) many chef suggest orange's vascular veins which look "fibrous" and have similar translated word with "fiber" itself.
Please enlighten me which?
Answer: Cellulose is one of the most common sources of fiber in the nutritional sense. Because oranges are plants, their cells have cell walls, made out of cellulose, so some of the fiber in an orange is surrounding each individual cell. Both vascular cells and pith cells tend to have particularly thick cell walls, so they are probably higher in fiber (this article also suggests that the pith is particularly high in fiber - vascular tissue is probably not mentioned because it is less prominent).

Which part of oranges contain fiber?


What is the source for a Bar Mitzva seuda?

Question: What sources are there for our minhag of doing a Bar Mitzva Seuda (meal), and do the sources state that the seuda must specifically be done on the day of the Bar Mitzva (or the night of)? And is this seuda actually a Seudas Mitzva?
Answer: See the Magen Avraham, Orach Chaim 225:4.
He points out a couple things:

It is a Mitzvah for the father to make a Seudah (festive meal) on the day his son turns 13 (enters his 14th year, i.e. not the evening he turns 13, but the next day). This is equal to the obligation to make a Wedding Seudah.
If the son makes a Drashah (Torah speech/lecture) in honor of his Bar Mitzvah, this is considered a celebration of the Bar Mitzvah (and the meal is therefore a Seudat Mitvah) even if it is not on the actual day.

The Magen Avraham quotes his sources, but I did not look them up.

See also the Zohar Chadash [Bereshit 15:4, according to here] quoted in footnote 697 here.

Cf. the following passage in Zohar Chadash, Parshas Bereishis: "R. Shimon Bar Yochai invited the leading scholars of the Mishnah to partake of a great festive meal which he had arranged.... He was very happy..., because, [as he explained,] 'On this day a holy and exalted soul descended...into my son R. Elazar, and on this joyous occasion I shall experience supreme joy.' "
Comment: Thanks. Although I think you may have made one mistake: when the boy turns 13, i.e. his birthday, that would already be the first day of his fourteenth year, no?
Comment: @phil. The Jewish day stars the night before, so the boy becomes bar mitzvah the night before. The Magen Abraham is saying not to celebrate that night but the next day.


Is it good practice to use Synthesia to figure out songs?

Question: Just wondering what pianists think about synthesia. You can type Synthesia followed by just about any song name you can think of on Youtube. ex "Synthesia bach minuet in g" and you'll get a Synthesia video that shows you exactly how to play it. I try to mainly figure songs out by ear so when I use Synthesia I feel like I'm "cheating", nonetheless it helps me sometimes. But is it bad practice to use or is it respected and used by advanced musicians for learning songs?
Comment: It's about the same as learning to speak a language vs. learning phrases from a phrase book. It can help you order your breakfast, but people can be disappointed when they realize that breakfast is *all* you can talk about.
Comment: A giant caveat no one mentioned: You're at the mercy of the ear-training skill of whomever uploaded the Synthesia video. Most of the extremely popular ones on Youtube with 99% likes have a ton of ridiculous mistakes!
Comment: @KilianFoth Though isn't part of speaking a language first learning the phrases? While learning to speak a language leads to being able to organically produce phrases, I imagine that along the way the first have to memorize rote phrases before they understand how they are formed.
Answer: It isn't bad practice. However you win your war you win.
Whether it is the best idea or not in the long term depends on your goals.
Just like learning guitar music with tabs rather than traditional notation there are advantages and disadvantages.
Some obvious advantages include:

You don't have to learn standard notation now
You get to hear the song while you go along
What ever other reasons you can think of for why you do it now.

The disadvantages are numerous.

you can only learn pieces that somebody bothers to prepare for YouTube. While you think just about any song is there I am willing to bet that that's not true. Also there would probably be only one or two arrangements of the song.
you aren't necessarily exposing yourself to technique building exercises. You might be but assuming you rely on this format only I doubt you'll be doing many scales and études
You'll be limited in what you can play with other musicians or even strangers. By learning standard notation and conventional methods for you chosen genre and instrument you develop the ability to get started with others with relative ease. Guitar players generally know how to follow a song by ear. Jazz players generally know how to follow a lead sheet etc.
Time - the biggest most significant disadvantage. Using any non written prerecorded format for learning music severely slows you down. If you miss something you have to manually use whatever interface to seek the point you missed. And repeating sections can only happen at the pace of the playback. Jumping along to similar passages based on similarity is slow. When reading you can basically instantly get to any point you want. You can also get an 'Aerial view' that would allow you to spot patterns and such.

If none of those advantages matter to you and you only want the easy way now so you can play a short piece for a talent show or something then you have the right tool in Synthesia.
Otherwise you really should put in the effort now and learn to at least kind of read written music. You'll be better for it in the medium/long term.
As for the respect part... I don't know for sure but I am willing to bet 'serious musicians' would shake their heads in disapproval. That's an obvious generalization but the music world is pretty well known for snobbery of all types. I recommend you don't worry about that.
When you are performing a piece literally nobody in the audience cares how you learned it. They just care how you play it there and then.
Edit Apparently it just uses MIDI files. Which reduces the impact of the first disadvantage. However one must still be able to either find MIDI files or prepare them for themselves. If you're going to go through the effort of converting transcribed music to MIDI, you'll be at least learning the note names of standard notation.
Comment: Regarding the first disadvantage, note that we can also generate such videos from MIDI file, which can be generated from music notation software such as Musescore. So at least it has slightly more available songs than just those on Youtube, which now includes songs available in some music notation software. =) (also there is also Linthesia, a free version of Synthesia for Linux, if price is a concern).
Comment: @Michael Le Barbier Grünewald I'm a big fan of tabs myself. I find them easier to read and just as information rich as standard notation. I'm making a case for written notation in general. I wish tabs were more popular, they're the bees knees. I've never seen what you describe. Have any links?
Comment: @xerotolerant [Wikipedia](https://en.wikipedia.org/wiki/Tablature) but I am not so much into that stuff that I can provide easily more example, but they exist. (My comment was a bit of tongue-in-cheek humour BTW ;) ) Also I think that baroque musicians used something similar to accord numbering, esp. for harpsichord accompaniment  – but I was not able to find pictures displaying this again.
Comment: One extra advantage: having a visual representation of what you're supposed to do is way more natural, easier to translate what you see into what you need to do. It's combined with advantage 1, but not the same.
Comment: I remember having seen notation very similar to tablature on ancient partitions (Baroque or Renaissance IIRC), which makes it quite unclear to me what you understand as traditional notation. ;)
Comment: @justhalf I put an edit in there, thanks for the info. I figured it used midi, because why wouldn't it? But the op didn't mention it so I assumed I was missing something.
Comment: Regarding "Using any non written prerecorded format for learning music severely slows you down", I've bizarrely found anecdotal evidence that some people find it easier and faster to learn pieces with Synthesia instead of regular sheet music in http://forum.ninsheetmusic.org/index.php?topic=8661.msg348749#msg348749 and http://forum.ninsheetmusic.org/index.php?topic=8678.msg349123#msg349123. (Admittedly, the second poster was still learning how to read sheet music.)
Comment: I'm not talking about the rate I'm talking about navigating the piece, going over sections and recognizing patterns. When my students transfer for memorizing pieces bit by bit aurally to reading there is always a 'remember how long that used to take?' moment.
Comment: @xerotolerant -- I don't understand how you can see tabs and staff notation as similarly information-rich. While tablature may be useful for communicating specific fingerings, especially for learners, there is no way to effectively communicate rhythm in tabs. I don't think that tablature is useless, but it all to easily becomes a crutch, and it isn't that hard to develop a basic facility reading staff notation.
Comment: @DavidBowling see http://www.guitarnick.com/amazing-grace-fingerstyle-guitar-tablature.html
triplets and quavers are notated just fine. Even in the text only ultra simple tabs on gametabs.net they still have their own notation for quavers and such. Granted that the text only one isn't great just using stems and beams tabs is pretty effective for timing in my book.
Comment: On disadvantage 4, I agree with the navigation part, but partially disagree with the patterns comment. For a visual learner like myself, it's pretty easy to spot patterns using tools like synthesia. So that disadvantage is real to some people but not others.
Answer: Synthesia is a program that plays and visualizes MIDI notes as "piano roll". The MIDI file itself is created based on a (supposedly original) sheet music, or otherwise arranged by its creator.
As a self-learner, between a sheet music and Synthesia, I'd separate learning into 3 types:

Sheet music: I think most won't argue that this is the best media to use if you want to learn and play a music. Sheet music is very expressive with their musical notations (e.g. dynamics, tempo, articulations), that are usually lost when translated into a MIDI file (read: the expressions themselves aren't lost per se, but human players will have a hard time to guess if a note is a staccato or just a very short 1/32 note.)
MIDI file: For auditory learners, MIDI file can help translate the sheet music into a sound that auditory players can "see" in their mind (or alternatively, "play by ear"). Players might be able to play the music without having the skill to read sheet music. However, they are locked into a certain playstyle depending on the creator of the MIDI file.
Synthesia/MIDI visualizer: For visual learners, these programs might certainly help them to know which notes to play without knowing to read the sheet music at all! However, just like with MIDI files, they are now locked into a certain playstyle; they won't know if a group of 5 notes is actually a trill, or actually just as-is on the sheet music (while Synthesia is capable of showing a sheet music based on MIDI, it's still only based on the final MIDI data. Compared to music notation softwares, it isn't capable to show musical notation like trills). Worse, Synthesia only shows the piano roll without any volume/tempo marking. This will only help them to know which notes to play, but not how.

My conclusion is, learn and read from sheet music, use MIDI file and/or Synthesia to help you, but don't fully depend on them.
As for "respect by advanced musicians", I don't have any data and can't answer that.
Answer: I can offer my perspective as an old school music gamer and amateur musician. I began playing (konami) music games in the arcade before you could play these things at home. The difference is back then it was a full body experience. The first game I played was called "Para Para Paradise", which is more of a "dance to the symbols" type of game. Within a couple of years I was a high level DDR player and I competed in national tourneys with my feet. I ended up spending about 10k in dollar coins playing DDR during my college years.
Synthesia is basically a more refined UI on the Konami Keyboardmania game system. The mechanics are exactly the same. The arcade version of Keyboardmania even had a pretty decent electric keyboard, though the number of keys was quite limited. I remember playing against real-world pianists in that game, and being blown away. I could never move my fingers that fast; I was a DDR kid.
But in the context of your question, I think I can answer unequivocally NO, I do not believe that you can really figure out songs this way. And there is a fundamental reason why.
At a high level of play there are a lot of players that can do things like memorize very complex songs and even play them backwards (i.e. with the keys reversed, and hands behind the back). The reason they can do this is the brain is only really responding to one stimulus at a time: the next key, or the next pattern. It's like memorising a speech from cue cards. You can do it, sure, but a lot of fluency is lost in the process. You're reciting the cue card... you're not actually "owning" the whole performance.
In order to own a performance it has to have a level of improvisation, it has to be based off your own "feel" of the music. Memorizing music tracking software has the effect of "dulling" the song, reducing it to notes. "Well people memorise music tablature all the time! How is it any different than that?" you might ask. And you're right, it's virtually the same. There is a little bit more subtlety in music tablature, but ultimately if you're playing music off of tabs you're also not really "getting it". The real understanding happens when you forget about the tabs and let your mind take control. Tabs also have the additional benefit that they have abstracted the form. Music tracking software is so literal and so explicit in its visualization that it leaves nothing to the brain to figure out, and I believe that makes the brain more dependent on the software and less able to understand the actual music. It seems easier because it is easier, only you don't want it to be easy. You want to learn the music.
Comment: so, what's the solution, playing by ear?
Comment: Repetition and study. Copying other people's music is not an exercise in musical expression, so if your goal is to copy a work faithfully, all that is required is that you *see* the patterns as they are. This requires a familiarity with the patterns in the first place, which are all derived from basic structures. Repeating and fully understanding "basic" musical structures reveals more advanced structures; makes them feel "obvious". You are playing by ear in the sense that you rely on your ear for judgement, but you ear must be trained at a level that it can recognize appropriate patterns.
Answer: As far as "respect by advanced musicians" goes. I know a few. Not many of them have heard of Synthesia, and those that have think it's "a cool idea, but I wouldn't use it." Judging by its original name, Piano Hero, Synthesia is meant to be a piano version of Guitar Hero. So, can you learn guitar through Guitar Hero? Somewhat, yes, but not fully. If you plan to have piano as a career, avoid Synthesia unless you are using it as a game, like you would Guitar Hero. If you are just an amateur pianist and want to learn how to play a few songs on your own, go ahead and use Synthesia. The other answers are quite helpful on this subject as well, going into more depth on the pros and cons of Synthesia.
TL;DR:
If you want to play with a band, don't use Synthesia.
If you want to learn a couple songs, and only that, use Synthesia.
if you want a career in music, don't use Synthesia.
Post-Scriptum: If you learn to read sheet music, and/or play by ear, you can learn songs much faster than you can through Synthesia. I myself can learn a basic song through sheet music in under 3 hours. I can master it in a month. Using Synthesia, I could never master it, and it would take me weeks to learn it.
Comment: I have to agree with @Patrick here. Perhaps if you want to compare with the guitar/bass counterpart, there's [Rocksmith](https://en.wikipedia.org/wiki/Rocksmith) which simulates... at least more than 5 buttons. Still, you got the point that these games are not the best learning tools.
Comment: "So, can you learn guitar through Guitar Hero? Somewhat, yes, but not fully."
Pointing out that Guitar Hero does not teach guitar, notes, or any type of music at all.  ".. they're just little plastic controllers. You hit the colored buttons and it makes the guitar track on the game play."
Answer: No, 'advanced musicians' would prefer to see the sheet music.  Synthesia would be considered  a very cumbersome method.  There may be occasions however where a notated version of a particular song was not easily available, Synthesia would certainly be better than nothing!  So thank you for bringing it to our attention.
Answer: You need to stop caring what other people think and get on with learning and mastering the things you want (in music and in life).  Any way or any tool that helps you learn to be a musician and enjoy the craft is fine.  Synthesia is another (great and fun) tool to help beginners master many aspects of music, most especially playing music.
It is not explicitly designed to teach you theory, but there are Synthesia scores and midi files that help you learn that.  Same for other aspects of music education.  By itself it is not enough, but combined with other things makes you a (better) musician.  Don't buy into the BS that many elitists push into learners' brains.  Enjoy yourself and learn.
You say I feel like I'm "cheating".  This is a feeling you have, like you feel happy, sad, shameful, or hungry.  Get over that and get on with learning.  Synthesia is modern technology that didn't exist when your great grandmother was learning piano and perhaps got her knuckles bloodied by some ignorant "advanced learner" for hitting the wrong keys on the piano. If you mastered a song well and played it for her, she would (or should) be delighted.  If she is not, then her negative feelings of jealousy or shame that interfere with her enjoyment of life.  Fix your feelings and elevate them to support you.  Take advantage of modern technology whenever you can, and don't let it substitute it for your own skills and knowledge.  You must "own" and develop your skills and constantly improve them.  Technology can assist, but not substitute for your skills when you are playing solo in public.
When you are older, (we all hope) you will lose the harmful mental habits of believing or caring what other people think.  I don't agree with @Gavin and some other posters who provide their opinionated answers for your question.  Should you really care to get "respect by advanced musicians"?  I am opinionated (everybody has a brain and an anus), and I say "NO".  If you a member of the society of elite musicians or similar circles of society, perhaps... and in the end, it comes down to performance.  For now, have fun learning, and you will pick up the theory and professional musician practices when you need them.
Answer: Synthesia is at its most helpful when fingerings are added to the notes. Otherwise, you need to have at least a fairly good sense of which fingers to use on a given piece. Also, many who use Synthesia never learn proper legato playing, nor how to use the pedal. They play like a gamer might play. Leaving the pedal down through the whole piece thinking it sounds great, then desperately touching each key in a mad attempt to get to 'em all before they disappear from the screen. Ultimately you want to play like you're feeling the music, not like you're gonna explode if you miss a note.
Those Synthesia tutorials showing overhead view of a real person's hands playing - those are probably a lot more helpful. Really study their hands and their playing if you've got to go the Synthesia route. I bet most of those guys themselves had been tutored by an actual teacher who gave them individual attention.
Answer: I believe as long as you're able to learn a song, then you're good. In my case, I can read sheet music perfectly fine, but I can learn songs much faster by listening to them and using Synthesia. This is not cheating as long as you learn the song right.
Now, since I find it harder to read sheet music, I can do daily sight-reading exercises to help improve my skills. What I recommend is to learn all the main songs you want to learn any way that is the best for you, and find a small and simple score online once a day to help you with sight-reading. Just look at the score for a minute or two, and get an understanding of the notes, the fingerings, the articulations, and the dynamics. Then, play the song slowly to see how it sounds. You may mess up quite a bit, or maybe not. It all depends on your sight-reading skills and the difficulty of the score. Also, if you feel it would help further, take another few minutes to learn how to play the song a little better until you learn it (I don't follow this approach because I want to expand my ability of being able to learn how to play a song the first time. Afterwards, it's just fine-tuning, and then later, nitpicking.).
Also, when it comes to Synthesia, I like it when it also shows the player's hands while the notes scroll down. I don't think these are as common online, but it helps me understand how I can play the song with my hands. It's almost like reading fingering numbers on your sheet music.
That's my advice. Happy playing!
Comment: Could you clarify on "Synthesia [...] also shows the player's hands while the notes scroll down"? I've never seen this, though I only tried the free version. Did you mean showing the left-hand/right-hand separation, showing the whole fingering number, or literally virtual hand playing the piano? Unless... did you mean a video of playback of Synthesia combined with a real human playing the piano?
Answer: Something people aren't considering is the accuracy of the transcription in the first place. This problem of course isn't limited to synthesia, but it is definitely a lot more prevalent. If I look up the most popular synthesia videos on Youtube, a large portion of them will have extremely ridiculous mistakes, including wrong chords that any trained musician can spot from a mile away, and even a non-musician could easily hear if given the accurate version for comparison. Sheet music will generally be free of mistakes if it's from an official source, but if it's some random person doing the transcription, it is subject to the same risk. Your playing will only be as accurate as the ear-training skill of the person doing the transcription.
Answer: from My non-traditional journey into music.
No formal lessons, no music reading, no piano in the house... somehow I got to the point of wanting to produce music.
When you learn a song on synthesia... It can help to see the chords. But, if you try to memorize an entire composition just by remembering every single note... this could be seen as trying to remember a human being by every single cell.
I have found by far the most progress in my musical journey when I understand enough to ask myself "why".
Why can some people play 10,000 note songs? It isn't because of synthesia. Is it because they understand the building blocks?
Actually, there are only 12 tones in western music. That is more simple than the alphabet. So, you can definitely learn it!
Answer: Synthesia is a good way to learn songs on the piano if you know enough music theory to understand the bigger picture of what's going on in the song. If you are familiar with all the concepts, you can basically watch the synthesia video a couple of times, and be able to play it without having to learn every single note from the video.
If you're only able to take away the individual notes being played in the video, I would recommend spending more to learning music theory, chord theory and ear training first.


4.3 OTA Update Install Fail With Motochopper Root 4.2.2 Google Nexus 7

Question: I am using Stock Android 4.2.2 on Nexus 7 2012 Tablet. I rooted my tablet using the Motochopper Root. I was able to download OTA 4.3 Update using normal procedure on my tablet however, when I tried installing the update, it just stuck at the android guy with error at startup. I tried downloading the OTA update again as it just disappeared, however it is stuck at waiting to download. I tried Nexus Tool Kit downloaded Stock 4.3 OTA and tried to install it using ADB sideload command. However it gave an error and mentioned some error file and exited. Please Help me out . I also tried full unroot with SuperSu but it also did not work.
Answer: Download stock ROM from Google, and flash it.
To check correct version for your Nexus 7 2012, see this question.
Since it would now be stock, you'd have to root it again.
Comment: @aibk01 If you can still connect your tablet to a PC and access the files in it, copy them. Otherwise, too late. It is recommended to always backup before doing something that might break your phone, like rooting or flashing a different ROM. I'm afraid you'll have to do a factory reset (in recovery mode) before flashing a new ROM.
Comment: I dont want to lose any data.
Comment: How do I achieve that??


Is it possible to upload an arduino sketch through the serial port (RX) instead of USB

Question: In another words, is it possible to develop a custom bootloader so sketches can be uploaded via serial connection made using the RX/TX pins and not via the USB connector (I am using Pro Micro boards)?
Thanks!
Comment: This is definitely possible. Bootloader is just a program which can communicate whatever hardware is available and write memory and jump to it.
Comment: This should be possible by adapting the serial bootloader typically used on the ATmega328p (etc) to your ATmega32u4.  The details of doing so however do not really fit in a question on a Stack Exchange site *unless you explain a specific difficulty*.  Make sure to do some searching, it is quite possible someone has already done this project.  Also consider if switching to an Arduino type board that simply has an ATmega328p (especially a compact one without a 2nd chip as a USB bridge, though you can bypass that) might be the simplest route to fill your need.
Comment: Makes sense, thanks for your answers, sorry I did make a search for that prior to asking but couldn't find any simple answer to this question.
Answer: No need to have a specific bootloader. The basic bootloader can do that (in Arduino that's the case so I hope this answer will apply in your case. But if not, the principle is certainly the same).
Once you perform a reset on the board, the bootloader look at the serial port during a short time. If something come, it checks if it's an hex file and if yes it send it to flash. The USB just use the RX input.
So you can send data using a direct connection or using for example a Bluetooh like HC-05. I do that for some project in order to update via Android: the Android app send an order to the Arduino, through Bluetooth.
Receiving this, the Arduino RESET itself, and then the Android App send immediatly data.
On Arduino side: connect for example A0 to RESET PIN and perform a digitalWrite(PIN_RESET,HIGH);
Have also a look at Reset an Arduino Uno in code
After the RESET, the board will reply with 0x14 0x10 (so it send this to TX and so if you have a bluetooh module, you'll received than on your Android App (eg))
You must then send  0x50 0x20 to the board to tell it you enter programming mode.
Then send 0x75 0x20 to get the id of the board in order to be sure you will send the HEX file for the right hardware.
You will receive 0x14 XXX 0x10 where XXX = id of the board
Then you can send the HEX file.
For that, you will send it by blocks of 128 bytes
So start by dividing the HEX to know the number of blocks then loop against this  number:
Start at ADR=0 (adresse dest in flash) and send:
For each block:
1) Send 0x55, low byte of ADR, high byte of ADR, 0x20
2) check reply (must be 0x14 0x10)
3) Send the 128 bytes: 0x64, 0x00, 0x80, 0x46 then the 128 bytes and finish by 0x20 (0x80 is the size)
4) check reply (must be 0x14 0x10)
5) update ADR. Take care: ADR is a word pointer (2 bytes). So ADR = ADR+0X40
Loop on num of blocks
Finish the job by sending 0x51 0x20 (exit programing mode)
Some details:

0x46 before the 128 bytes tells you want to write in flash. Other codes are available eg for checking, getting data etc..

It seems mandatory to send each time 128 bytes. So if your last block is smaller, you need to add some '\0' to get a total of 128. I've been unable to get good results trying to change the 0x80 value and send less bytes. :(

It's not very easy and need tests to get a good code but that really fine to be able to have an Arduino the user can update.
Hope this will help.
Answer: Yes. You can develop a bootloader for the ATmega32u4 that will receive firmware over any interface (UART, SPI, I2C etc.).
Loading via UART is a solved problem. Look for the AVR109 bootloader.
Answer: Yes, there is an Optiboot fork supporting ATmega32U4 supporting hardware UART to upload Arduino sketches.
Also, a detailed instructable post explaining how to use it with Arduino Pro Micro.


How Long Did it Take Superman to get to the Earth?

Question: How many Earth years did it take the rocket from Krypton bearing the infant Kal-El to reach Earth?
Comment: In which continuity? The 4 film series', the 10+ comic origin stories or the 6 TV series?
Answer: The references below all appear to base their info on the first Christopher Reeves movie.
According to this link, the flight took two years.
However,  according to this link and this link, the flight took three years.  Don't know if one Wiki derived it's info from the other or if they both independently derived info from the movie.  Unfortunately, I don't have copy of the movie to check it out myself.
One thing I seem to recall from  the move is the image of Jor-El (when his image first appears in the fortress of solitude) tell Kal-El (Superman) that thousands of years would have passed on Krypton.  If that's a reasonably accurate memory, would imply that the 2-3 flight time years experienced by the infant Kal-El were either a time-dilated measure or that Kal-El passed through some type of wormhole where the two ends were in different times.  But that's pure speculation on my part.
Answer: At the speed of light, the length of time experienced by the baby would be a couple of years, but outside of the ship, where the time dilation does not occur, 20,000 years or more would have passed.
So, it took 20,000 years or so to reach Earth, but the baby only aged 2 years in the time protected ship.
I recall an origin story where Jor El and Lara are discussing Earth and Jor El mentioned that by the time Kal reached the planet, its inhabitants will have evolved into organized societies.
Comment: Where are you getting the factor of 20,000? At the speed of light, time dilation would be infinite...
Answer: This answer is based on the Superman radio serial episodes available at the Internet Archive.
In episode 1 (February 12, 1940) we learn that the planet Krypton is in our solar system

Narrator: "As our story begins, we ask you to come with us on a far journey, a journey that takes us millions of miles from the Earth where the planet Krypton burns like a green star in the endless heaven."

and in fact is a Counter-Earth:

Jor-El: "A planet smaller than our own, situated on the other side of the sun."

From this one would expect that the journey would take some months, at most a couple of years. However, in episode 2 (February 14, 1940) we learn that it took much longer than that, something like 20 years if we assume that Kryptonians grow up at about the same rate as Earth people:

Narrator: "During the long journey of the rocket ship to the Earth, the child has become a man. The rocket landed in a [???]. Superman stepped forth full grown to explore this strange new world in which he found himself."
Comment: "In our solar system" ... when I was a kid, watching the Superman TV series, my mom told me about the origin story for Superman.  Either she said it, or I just got the impression: the current asteroid belt of our solar system is the remnant of that lost planet.
Comment: A counter earth is possibly the only good explanation for so much Kryptonite landing here.
Answer: Hypothetically 200000 passed by Planet Krypton's timepassing standards inside its area, but the timepassing flight lasted about 3-2 years which means that the flight tranportation which carried Superman traveled somehow faster than speed of light theoretically creating a wormhole according to my thoughts. So, it made Superman arrive at modern Planet Earth.
Comment: What are you basing any of these numbers on? Is this sourced in any comics or movie?
Answer: Lex Luthor stated in the first movie, that it took the ship three years to reach Earth.
Comment: Hi, welcome to the site. This answer is correct, but you could improve it by editing it to include an exact quote, which you could copy and paste from an online script. To further improve this answer, you could also add a video clip from YouTube; I believe there is one of this specific scene.
Answer: Well obviously it took 2 years because by then if he been on that thing for 3 years he could probably talk. Plus it said in the ultimate guide that he was an infant not a toddler
Answer: In 'Man of Steel' with Henry Cavill, humans find Zod buried in ice nearly 20,000 years old. Also, in the movie Zod is sentenced to Somatic Reconditioning soon after "Superman" is sent away like a baby Moses on a cosmic river. So yeah, there would have to be some worm-hole time-loop going on if it only took 2-3 years for Kal-El to get to Earth.
Comment: Humans found a seed ship. They did not find Zod in "Man of Steel", Zod came to Earth in response to Clark activating the ship
Comment: I don't understand you. Can you not use short forms?