What is the technically correct term for this? oxygen endurance? oxygen autonomy? Trade (talk) 05:14, 17 March 2025 (UTC)[reply]

A SCUBA diver calculates the time he can work on the available gas, called endurance from: Available time = Available gas / RMV (Respiratory minute volume) where RMV is the volume of gas that he breathes in a minute. RMV depends on many factors and may be 35 L/min for a working dive without assistence of rebreather equipment that can both extend the breathing endurance of a limited gas supply and, for military frogmen conceal the release of gas bubbles.A Life-support system for humans in hostile environments such as outer space or underwater must maintain adequate pressure of Breathing gas that has neutral gasses added to oxygen that would in isolation be toxic. Philvoids (talk) 09:28, 17 March 2025 (UTC)[reply]

(edit conflict) If we are given the specs of the vehicle or other enclosed system including its oxygen supply, the answer still depends on the number, kinds and sizes of life forms present and their oxygen demands (e.g., whether they need to be involved in energetic activities). Where a crew of three burly humans would die for insufficient oxygen in ten minutes, a single modestly-built person could remain alive for more than half an hour, and a trudging of tradigrades could hang on forever.  ​‑‑Lambiam 09:31, 17 March 2025 (UTC)[reply]

Here's an actual example Rescue of Roger Mallinson and Roger Chapman. When a submarine is trapped on the seabed the crew may repeatedly run from one end to the other to release it. Nobody knows why this manoeuvre works. 2A00:23C7:E53F:2901:78F1:95EF:27E8:7847 (talk) 10:23, 17 March 2025 (UTC)[reply]

@Philvoids and Lambiam: IMVHO your replies have nothing to do with the question. Trade doesn't ask what factors determine the time a person can live in air-less environmet or what devices are used for it. The question is "what is the technically correct term for a maximum time a vehicle can sustain life of its crew" with no external air or oxygen supply. --CiaPan (talk) 12:02, 18 March 2025 (UTC)[reply]

I tried (but apparently failed) to explain that one should not expect such a term to exist since this time is a function of too many factors. Any statement of a form like "the maximum time the K-141 Kursk could sustain life using its onboard oxygen supply was 24 days" is bound to be nonsensical.  ​‑‑Lambiam 12:53, 18 March 2025 (UTC)[reply]

@CiaPan Thank you for restating the question in your own words. Without mock humility I qualify the term that I offered ( "breathing endurance" ) as irresponsible for anyone to quote as an implicitly guaranteed time in any of the high-risk missions listed in the question without conveying an understanding of the real-world factors involved. Documented life support accidents should have taught us that expected and actual survival times can differ greatly, and that prolonged Asphyxia (oxygen deprivation) does not cause an abrupt irrecoverable death. There is no good term for unwillingness to resuscitate lives by Artificial ventilation such as mouth-to-mouth insufflation, Philvoids (talk) 15:05, 18 March 2025 (UTC)[reply]

Reading the page on Taxicab geometry, it is easy to understand how distance between coordintates is not the same as Euclidean distance. I have searched and have not found any examples of situations in which using taxicab distance in data analytics is preferred over using Euclidean distance. I found many examples of various metrics, such as when cosine similarity is preferred over Euclidean distance. So, is there an example of when I would compare the attributes of two objects using taxicab distance that is not the already given case of seeing how far apart two intersections are in taxicab space? I have been thinking about this for a while and I came up with an idea that I believe would work. In tennis, you are either serving to score or defending and trying to take over the serve. You are never both. So, if I were to compare tennis players based on total number of times they have served to total number of times they've received the serve, those two attributes are exclusive of one another. You cannot add one to both of them at the same time because nobody can be serving and receiving a serve at the same time. But, I fear that I have a grave misunderstanding of taxicab distance. 68.187.174.155 (talk) 19:25, 17 March 2025 (UTC)[reply]

The chapter "Distances and Similarities in Data Analysis" in the book Encyclopedia of Distances mentions this only under the heading "Penrose size distance".^[1] For ${\displaystyle n}$-dimensional space the Penrose size distance differs from the taxicab distance by a fixed factor of ${\displaystyle {\sqrt {n}},}$so for purposes of data analysis it seems equivalent to me. Google Book Search yields some examples of applications of the Penrose size distance, which I have not attempted to investigate further.

As to your tennis example, both of these numbers, serves and receives, will be higher for players who have played many games than for beginning players, so to make a somewhat meaningful comparison one should make these numbers relative. For example, if S is the number of serves and R the number of receives, one might assign a player a score of 100 S / (S + R). Now we have single numbers. For an actual comparison this is not a good measure, since much depends on the strengths of the opponents a player has met. (Compare the Elo rating system for chess.)  ​‑‑Lambiam 11:02, 18 March 2025 (UTC)[reply]

The subject is calculating the distance between two point coordinates on Earth. A ship's or airplane's intercontinental navigator gets the correct answer that accounts for our planet's near-spherical curvature from the Haversine formula. For most local purposes the Euclidean distance that is the line length that a bird flies assuming level flight over a flat earth is accurate enough. City taxis cannot fly like birds and their routing is better measured in Taxicab geometry where the effective distance between points is found by accumulating the typical (for say, a a grid-oriented metropolis such as Manhattan) block lengths driven between the points. The taxicab distance exceeds the Euclidean distance because of the necessary Quantisation of ground distance in coarse units of block size. (Smaller blocks reduce the overestimation and allow a smoother taxi trip.) I suggest no useful understanding of this subject comes from Tennis scoring rules or the complication of one-way city street routing and that the taxicab distance calculation (if not the fare charged) is the same in either direction. Philvoids (talk) 11:21, 18 March 2025 (UTC)[reply]

(Smaller blocks reduce the overestimation and allow a smoother taxi trip.)

Yet the taxicab distance remains the same.

Greglocock (talk) 23:33, 18 March 2025 (UTC)[reply]

Since both distances are independent of the block length, so is the overestimation.  ​‑‑Lambiam 08:12, 19 March 2025 (UTC)[reply]

No. My throwaway comment in parenthesis implies that demolishing Manhattan and rebuilding the area using smaller blocks would allow shorter taxi routes. It is undeniable that finer quantisation would reduce the quantisation error that I call overestimation of the birdflight distance. Morals to be drawn from this are A) do not rely on taxi charge meters for ground distance measurement and B) there can be practical objections to demolishing Manhattan. Seek legal advice first. Philvoids (talk) 11:29, 19 March 2025 (UTC)[reply]

If the "streets" run parallel with the x- and y-axes, the Manhattan distance between two points with coordinates ${\displaystyle (x_{1},y_{1})}$and ${\displaystyle (x_{2},y_{2})}$equals ${\displaystyle |x_{1}-x_{2}|+|y_{1}-y_{2}|.}$The length of a block has no role in this expression.  ​‑‑Lambiam 17:04, 19 March 2025 (UTC)[reply]

If both points lie at crossroads your integer math suffices. Philvoids (talk) 15:47, 20 March 2025 (UTC)[reply]

The usual definition is for ${\displaystyle (x,y)\in \mathbb {R} \times \mathbb {R} ,}$but works equally well on ${\displaystyle (\mathbb {Z} \times \mathbb {R} )\cup (\mathbb {R} \times \mathbb {Z} ).}$ ​‑‑Lambiam 18:57, 20 March 2025 (UTC)[reply]

That is what I thought. You can change east/west or you can change north/south. That appears important if using taxicab geometry to measure difference. So, I have preoccupied with trying to think of real-world situations where I want to measure the difference between two attrubute sets, but there is a catch. Within the attribute sets, you have one attribute that, if you are changing it, you cannot change the other. I am not trying to claim it is a smart thing to use taxicab distance. I was simply trying to think of a use for taxicab distance that isn't taxicabs in Manhattan. 68.187.174.155 (talk) 23:35, 19 March 2025 (UTC)[reply]

Several different data-entry interfaces have a variant of this. Example: using sliders or +/- numerical scrolls to change an RGB color. To go from red to blue, you have to take some sort of detour through darker red and then darker blue or via a range of magentas and possibly a total of 510 changes. Example: changing the four-digit squawk code on an older transponder where each digit has its own knob. I have a vague memory of a pilot accidentally reporting a hijacking because he changed from one innocuous code to another but left it in transmit mode and his choice of the order of the knob use passed through 7500. DMacks (talk) 01:12, 20 March 2025 (UTC)[reply]

The two answers here appear (to me) to imply that taxicab "distance" is not a thing. We can use taxicab geometry to make distances between points more granular. However, there isn't a practice of using taxicab distance in the same way I would use Euclidean distance or Jaccard similarity to calculate how similar objects are when doing something like clustering. Is that correct? 68.187.174.155 (talk) 18:14, 18 March 2025 (UTC)[reply]

Some of the GBS hits for the link I gave above use the Penrose size distance for clustering. If the definition in the first source I linked to is correct this is functionally equivalent to the taxicab distance. Somehow they are all about data from measuring teeth. (The eponym is Lionel Penrose.)  ​‑‑Lambiam 18:44, 18 March 2025 (UTC)[reply]

I think I am finally beginning to understand the concept. With Manhattan distance (p=1), having two (or more) metrics with the same value has more weight than just being similar. In other words, comparing (0,0) to (0,5) is more similar because x=0 on both compared to (3,4) where neither x or y is the same. But, in Euclidean distance (p=2), both have a distance of 5 because there is no weight on having the same value for attributes. It is less a "you can only change one attribute at a time" and more "if you have the same value for an attribute, the similarity will be higher." If you take that to the extreme of p=infinity, it doesn't even matter what most of the attributes are. Only the maximum distance matters. 68.187.174.155 (talk) 16:08, 20 March 2025 (UTC)[reply]

(The ${\displaystyle p}$here refers to the parameter of the so-called ${\displaystyle L^{p}}$-norm.  ​‑‑Lambiam 18:51, 20 March 2025 (UTC))[reply]

Manhattan Lp space? DMacks (talk) 00:28, 21 March 2025 (UTC)[reply]