logic – Does the existence of Gödel universal functions make the S-m-n theorem unnecessary?

The problem of deciding, for any $x$, whether $phi_x$ is a constant function, is undecidable. I came across the following proof of this fact in Rogers’ book:

enter image description here

To me, it looks too bulky and unnecessarily complicated (things like the unnecessary (I think) use of the S-m-n theorem, the introduction of this weird function $gh_1$…). I think if one uses the existence of a Gödel universal function, it makes the proof much more clear (and shorter). Namely, define the partial function $V:Ntimes Nto N$
by (see the definition of $K$ below) $$(q,x)mapsto 1 text{ if $qin K$} \ (q,x) text{ is undefined if $qnotin K$}$$ This is a computable function by the Church-Turing thesis (a program that computes it would accept a pair $(q,x)$ (if this pair is coded as one number, it would decode it), run $phi_q(q)$; if it stops, the output would be one; if not, then it would run forever). Now let $U$ be a Gödel universal function. Then there exists a total computable $s:Nto N$ such that for all $q,tin N$, $$V(q,t)=U(s(q),t).$$ Now $K={q:phi_q(q)text{ halts}}$ is $m$-reduced to ${x:phi_xtext{ is constant}}$ via $s$. Thus the latter set is unsolvable.

If this proof is correct (is it?), it makes me wonder if one can forget about the S-m-n theorem and only remember the existence of Gödel universal functions. Is it some kind of archaic result? Another thing that make me think this way is that there exist textbooks in computation theory (more modern than Rogers’ book) which do not make any explicit mention of this S-m-n theorem, but they use these Gödel universal functions quite a bit.

Cleanest way to delete the intersection’s unnecessary parts in Blender?

I’ve created a straight half tube model, and I’d like to combine 2 of them, to make a cross shaped tube.

How could I remove the intersection’s unnecessary parts to make the cross shape look… normal?

enter image description here

Unity: prefab export includes many dependencies on unnecessary resources

I come exported one of my assets in a unitypackage.
He understood all the dependencies very well so that I could use them.

Then I tried another prefab but he understood a lot of unrelated assets from everywhere in the project, it's a very simple prefab and I don't know how the bulk is considered dependencies.

When I do show dependencies it brings up the clutter in the project menu. In no case should there be dependence. It really is not as complex as a prefab.

I also checked the prefabricated elements to see if some of them somehow use the clutter said, they are not.

How can this happen? Is there a way to fix it (other than a selective click in the export menu)?

How to get rid of unnecessary Google Search Console URLs?

66 pages from my website that are all deleted still appear in the Google Search Console page report. enter description of image hereMy eagerness is to know all the possibilities. Questions include: 1. Does it affect SEO? 2. How can I get rid of these URLs completely?

[ Politics ] Open question: has this unnecessary and unnecessary quarantine gone too far?

The lock did nothing; deaths have doubled, confirmed positive cases have tripled … even quadrupled. The miserable virus would spread and people would be infected and still die.
All of this is just a ploy from our corrupt and foolish governments to lead the economy to hell, make everyone suffer in prison and prevent 100 years from dying. It is not about keeping hospitals "overwhelmed", as there are many beds and rooms in hospitals.

The real world, when it comes back, will only be cavemen, no jobs, no schools, no entertainment, no sporting events and the paranoia of a " second or third wave ".

And worse, the stupid sheep are "totally cool" with that.

algorithms – Identification of unnecessary vertices in an oriented graph

I have a randomly generated directed graph with 3 types of vertices: input, output and the rest (I'll call them hidden).

A useless summit is a hidden vertex which:

  • cannot be reached from an entry vertex, OR
  • cannot reach an exit peak.

For example:

  • entry = yellow / green
  • output = blue
  • hidden = white
  • useless = red border

Example of graph

Note that:

  • cycles and auto-loops are allowed
  • the graphic can be separated
  • inputs and output nodes are known (i.e. you can determine which type of node an edge connects to and from which)

So what do you call this type of problem? Is there an algorithm for this?

I am looking for more information on this. I have a python script that seems to be working. I'm just not sure it will work for all cases, as I don't fully understand it myself. This was a mix of DFS, trial and error, manual manual checks, and a bunch of if statements.

windows os – Why do so many software authors insist on forcing their users to do unnecessary work while updating their software?

Lots of software, such as Notepad ++, pgAdmin 4 and Bisq, which are all open source and free, without any attempt to install malware / spyware in the installer, make the unnecessarily boring update.

Instead of just seeing a message like:

There is a new version available: 1.2.3. You are currently running 1.2.2. Update now? (Yes) (No)

And then just update by pressing "Yes" …

Instead, they pester you that an update is available, but when you agree, it downloads a new installer or just loads a web page where you have to manually download the installer ;installation. Either way, once you run this new installer, it treats you like a "first-time customer", like it was 39; initial installation, making you look at a GUI and manually click "next" several times for seemingly no reason.

Why wouldn't it, since it is already installed on the computer, detect it (or launch with a flag such as "/ update") and simply update instead of display unnecessary stuff from the GUI installer that I already went through during the initial installation of the Software?

For software developed by fraudulent companies, the reason is obvious: they have another chance to trick you into forgetting to disable their toolbars / spyware / malware by checking the checkbox again. However, I'm talking again about those FOSS programs that don't use such tactics.

There is no logical or technical reason for this that I can think of. It is as if they are "punishing" the user by making us do unnecessary work to waste our time and energy. Having been faced with this for over 20 years, I'm absolutely exhausted from manually processing update after update after update, and I can't believe they haven't automated this thing very obvious and simple after so long, instead of putting their users through over and over again.

This practice strongly discourages upgrading, and I have often stayed with old versions for a very long time simply because I cannot handle clicking on another unnecessary installer.

And no, I don't want to use and trust third-party "Chocolatey" software. I ask why real software developers do this.

And no, it doesn't require any more work from the developers. Again, I'm talking about how the installer shows up and takes me through unnecessary steps for no reason since the software is already installed, and everything that the installer ends up doing is just to copy the new files to my existing installation directory. There is no reason to do this because the software is already installed and it clearly knows what to do already as I can simply click "Next" several times and then it updates.

The problem is that the installer shows that it makes no sense, as it is an update and not a "new installation".

Why do they insist on doing this?

api – Apparently unnecessary request for, or} at the end of the JSON file

This file contains information about Ed Sheeran's songs. I gathered the data with the spotify API.

"0":{"name":"I Don't Care (with Justin Bieber)", "data": {"type": "audio_features", "tempo": 101.956, "key": 6, "loudness": -5.041, "danceability": 0.798, "speechiness": 0.0442, "uri": "spotify:track:0hVXuCcriWRGvwMV1r5Yn9", "id": "0hVXuCcriWRGvwMV1r5Yn9", "acousticness": 0.0912, "valence": 0.842, "mode": 1, "time_signature": 4, "track_href": "https://api.spotify.com/v1/tracks/0hVXuCcriWRGvwMV1r5Yn9", "liveness": 0.0894, "analysis_url": "https://api.spotify.com/v1/audio-analysis/0hVXuCcriWRGvwMV1r5Yn9", "energy": 0.675, "duration_ms": 219947, "instrumentalness": 0},
"1":{"name":"Beautiful People (feat. Khalid)", "data": {"type": "audio_features", "tempo": 92.977, "key": 5, "loudness": -8.113, "danceability": 0.64, "speechiness": 0.187, "uri": "spotify:track:70eFcWOvlMObDhURTqT4Fv", "id": "70eFcWOvlMObDhURTqT4Fv", "acousticness": 0.124, "valence": 0.548, "mode": 0, "time_signature": 4, "track_href": "https://api.spotify.com/v1/tracks/70eFcWOvlMObDhURTqT4Fv", "liveness": 0.0802, "analysis_url": "https://api.spotify.com/v1/audio-analysis/70eFcWOvlMObDhURTqT4Fv", "energy": 0.648, "duration_ms": 197867, "instrumentalness": 0},
"2":{"name":"Perfect", "data": {"type": "audio_features", "tempo": 95.05, "key": 8, "loudness": -6.312, "danceability": 0.599, "speechiness": 0.0232, "uri": "spotify:track:0tgVpDi06FyKpA1z0VMD4v", "id": "0tgVpDi06FyKpA1z0VMD4v", "acousticness": 0.163, "valence": 0.168, "mode": 1, "time_signature": 3, "track_href": "https://api.spotify.com/v1/tracks/0tgVpDi06FyKpA1z0VMD4v", "liveness": 0.106, "analysis_url": "https://api.spotify.com/v1/audio-analysis/0tgVpDi06FyKpA1z0VMD4v", "energy": 0.448, "duration_ms": 263400, "instrumentalness": 0},
"3":{"name":"South of the Border (feat. Camila Cabello & Cardi B)", "data": {"type": "audio_features", "tempo": 97.986, "key": 9, "loudness": -6.376, "danceability": 0.857, "speechiness": 0.0824, "uri": "spotify:track:4vUmTMuQqjdnvlZmAH61Qk", "id": "4vUmTMuQqjdnvlZmAH61Qk", "acousticness": 0.148, "valence": 0.668, "mode": 0, "time_signature": 4, "track_href": "https://api.spotify.com/v1/tracks/4vUmTMuQqjdnvlZmAH61Qk", "liveness": 0.0865, "analysis_url": "https://api.spotify.com/v1/audio-analysis/4vUmTMuQqjdnvlZmAH61Qk", "energy": 0.621, "duration_ms": 204467, "instrumentalness": 0},
"4":{"name":"Shape of You", "data": {"type": "audio_features", "tempo": 95.977, "key": 1, "loudness": -3.183, "danceability": 0.825, "speechiness": 0.0802, "uri": "spotify:track:7qiZfU4dY1lWllzX7mPBI3", "id": "7qiZfU4dY1lWllzX7mPBI3", "acousticness": 0.581, "valence": 0.931, "mode": 0, "time_signature": 4, "track_href": "https://api.spotify.com/v1/tracks/7qiZfU4dY1lWllzX7mPBI3", "liveness": 0.0931, "analysis_url": "https://api.spotify.com/v1/audio-analysis/7qiZfU4dY1lWllzX7mPBI3", "energy": 0.652, "duration_ms": 233713, "instrumentalness": 0},
"5":{"name":"Photograph", "data": {"type": "audio_features", "tempo": 107.989, "key": 4, "loudness": -10.48, "danceability": 0.614, "speechiness": 0.0476, "uri": "spotify:track:6fxVffaTuwjgEk5h9QyRjy", "id": "6fxVffaTuwjgEk5h9QyRjy", "acousticness": 0.607, "valence": 0.201, "mode": 1, "time_signature": 4, "track_href": "https://api.spotify.com/v1/tracks/6fxVffaTuwjgEk5h9QyRjy", "liveness": 0.0986, "analysis_url": "https://api.spotify.com/v1/audio-analysis/6fxVffaTuwjgEk5h9QyRjy", "energy": 0.379, "duration_ms": 258987, "instrumentalness": 0.000464},
"6":{"name":"Thinking out Loud", "data": {"type": "audio_features", "tempo": 78.998, "key": 2, "loudness": -6.061, "danceability": 0.781, "speechiness": 0.0295, "uri": "spotify:track:1Slwb6dOYkBlWal1PGtnNg", "id": "1Slwb6dOYkBlWal1PGtnNg", "acousticness": 0.474, "valence": 0.591, "mode": 1, "time_signature": 4, "track_href": "https://api.spotify.com/v1/tracks/1Slwb6dOYkBlWal1PGtnNg", "liveness": 0.184, "analysis_url": "https://api.spotify.com/v1/audio-analysis/1Slwb6dOYkBlWal1PGtnNg", "energy": 0.445, "duration_ms": 281560, "instrumentalness": 0},
"7":{"name":"Happier", "data": {"type": "audio_features", "tempo": 89.792, "key": 0, "loudness": -7.355, "danceability": 0.522, "speechiness": 0.0288, "uri": "spotify:track:2RttW7RAu5nOAfq6YFvApB", "id": "2RttW7RAu5nOAfq6YFvApB", "acousticness": 0.536, "valence": 0.236, "mode": 1, "time_signature": 4, "track_href": "https://api.spotify.com/v1/tracks/2RttW7RAu5nOAfq6YFvApB", "liveness": 0.135, "analysis_url": "https://api.spotify.com/v1/audio-analysis/2RttW7RAu5nOAfq6YFvApB", "energy": 0.385, "duration_ms": 207520, "instrumentalness": 0},
"8":{"name":"Galway Girl", "data": {"type": "audio_features", "tempo": 99.943, "key": 9, "loudness": -3.374, "danceability": 0.624, "speechiness": 0.1, "uri": "spotify:track:0afhq8XCExXpqazXczTSve", "id": "0afhq8XCExXpqazXczTSve", "acousticness": 0.0735, "valence": 0.781, "mode": 1, "time_signature": 4, "track_href": "https://api.spotify.com/v1/tracks/0afhq8XCExXpqazXczTSve", "liveness": 0.327, "analysis_url": "https://api.spotify.com/v1/audio-analysis/0afhq8XCExXpqazXczTSve", "energy": 0.876, "duration_ms": 170827, "instrumentalness": 0},
"9":{"name":"Castle on the Hill", "data": {"type": "audio_features", "tempo": 135.007, "key": 2, "loudness": -4.868, "danceability": 0.461, "speechiness": 0.0989, "uri": "spotify:track:6PCUP3dWmTjcTtXY02oFdT", "id": "6PCUP3dWmTjcTtXY02oFdT", "acousticness": 0.0232, "valence": 0.471, "mode": 1, "time_signature": 4, "track_href": "https://api.spotify.com/v1/tracks/6PCUP3dWmTjcTtXY02oFdT", "liveness": 0.14, "analysis_url": "https://api.spotify.com/v1/audio-analysis/6PCUP3dWmTjcTtXY02oFdT", "energy": 0.834, "duration_ms": 261154, "instrumentalness": 1.14e-05}

The error I get indicates a "," or "}" was expected at the end of the file.

Bitcoin core – what prevents people from adding unnecessary blocks to very old blocks in order to roll back on new transactions?

As far as I know, network nodes should accept the longest branch of blocks and ignore all other branches (excuse my terminology if this is not what is normally used – I hope that what I mean is clear).

If that is correct, I wonder what would prevent me from creating my own node in which I add blocks to very old blocks. These added blocks may contain transactions from my address to another of my addresses for example (just to make sure the block is valid – I guess there are constraints on what makes a block valid , such as the amount of transactions or bits in a block). After probably a long time, I will have a branch that has exceeded the current branch, canceling all transactions from the block with which my node started to the current active block, and replacing all these transactions with my unnecessary transactions.

What is stopping me from doing this? I know I should still be exploiting these blocks, and I understand that it would probably be the main thing that would keep me from doing it now.

However, as I understand it, the difficulty of extraction is determined by the amount of blocks extracted in a certain time. Suppose the BTC network becomes useless one day for some reason, and almost no new block has been created, would it then be possible to run it (after a while to maintain the difficulty of my own weak mined blocks)

Thanks for all the answers in advance. If the BTC becomes obsolete and unused, it would be cool to be able to magically erase everything (if there are still nodes around).

mysql – unnecessary API calls to the disadvantages of external sites

I worked in a website before 3 years at the time, I wrote code to update 2 fields in the database. I got the value of the fields from an external API. I had to pass company_id for this API to get the answer. I have almost 2000 resource identifiers and 63 business identifiers in my database. I looped the resource identifiers and called 2000 times the external API and saved the data in db. Now before 2 days I saw the code and felt it to be incorrect and changed, now the request has been reduced to 63. I want to know if this affects the API site external in any way. Does it increase the load?