1

Physics, Astronomy & Cosmology / Re: What happens when photons leave the sun?

« on: Yesterday at 18:37:57 »

Hi.

   It's not the same photon that exits from the sun as the one that might have started in the core.   That's the main thing that explains why the journey has taken so long.   Also there are widely varying estimates of the average journey time -  from a few thousand years to a million years.

In the core of the sun the protons and helium nuclei are so thick that an emitted gamma ray can't get very far before it is absorbed. If you imagine that a gamma ray is emitted right at the center of the sun then it will start out heading right for the surface. When it crashes into a proton the result of the collision is a proton with extra energy. The proton gives up that extra energy by emitting another gamma ray photon. But this one could head in any direction -- even right back where it started from. And so it goes, with the gamma ray heading from one collision to another, changing its direction each time it is absorbed and re-emitted.

https://sciencing.com/long-photons-emerge-suns-core-outside-10063.html

     Although they make the whole thing sound poetical by referring "the gamma ray",  it's clearly been absorbed  (it has gone, there is no gamma photon to be found for a while)  and  some other photon was re-emitted - this has happened several times over.

    In between collisions the gamma rays travel at a speed that is either c (the speed of light in a vaccum),  or else the speed of light through the medium (generally slower).   Exactly what speed it has travelled at depends on how complicated you want to get and whether you wish to consider a group velocity or a phase velocity for light waves.  Explaining group and phase velocity is beyond the scope of one thread.   
     The propagation of light in plasma is complicated and apparently still under research.  The older thinking is that plasma should slow light down and indeed it's almost completely opaque to EM radiation in the visible spectrum.   However, just to turn this upside down, there are some new articles suggesting that you can actually get the group velocity (but not the phase velocity) to go higher than c in some situations.   (https://www.sciencealert.com/pulses-of-light-can-break-the-universal-speed-limit-and-it-s-been-seen-inside-plasma ).

   Finally, the gravitational potential and the over-all redshift issue is also complicated.   As @Halc  mentioned the change in potential is what will be important    BUT....   the potential energy at the centre of a sphere (the sun) is a topic which might spill over to another thread.   So we probably do need to know exactly how deep within the sun the photon was when it was created.

Best Wishes.

2

Physics, Astronomy & Cosmology / Does a gyroscope still fall in opposition to the direction of the missing force?

« on: Yesterday at 12:01:08 »

Hi.

    I was looking through some of the old Feynman lectures and came across this section which attempts to explain what makes a gyroscope start to precess instead of falling.   Just to be clear, it does not suggest this is what sustains precession, just what starts it.   You have a situation with a spinning gyro supported on a pedestal at the centre and you are holding the (soon to be) free end stationary with your hand until it is suddenly released.

gyro.JPG (28.45 kB . 583x312 - viewed 109 times)

This is what the lecture states:
     Some people like to say that when one exerts a torque on a gyroscope, it turns and it precesses, and that the torque produces the precession. ........it does not fall under the action of gravity, but moves sidewise instead!  .....( but ).........
    .....The gyro actually does fall, as we would expect. But as soon as it falls, it is then turning, and if this turning were to continue, a torque would be required. In the absence of a torque in this direction, the gyro begins to “fall” in the direction opposite that of the missing force.....

[End of section 20-3,  "Rotation in Space", Feynman lectures.
https://www.feynmanlectures.caltech.edu/I_20.html ]

      I can't be the only one who finds the idea of a "missing force" a bit odd.   To say that things accelerate in the direction of a net force is one thing,   to say that they would accelerate in the opposite direction to a missing force is much harder to live with.
     There's a computer on my desk and it is missing a force to move it left but it does not accelerate to the right.

    Anyway, is this explanation with "missing force" still popular?   At the moment I'm inclined not to recommend that explanation.   Maybe Feynman tried to oversimplify and has ended up with something that isn't all that usefull for understanding?   i.d.k.   I do note that he has quotation marks around "fall" as if he was just making an analogy to objects falling when they are missing a force to support them. 

Best Wishes.

LATE EDITING:  Fixed various spelling errors.   Title changed from "in the direction" to "in opposition to" etc.

3

Just Chat! / Re: Should we report all people to the police if we find them with child porn?

« on: Yesterday at 00:57:51 »

Hi.

You seem to have answered your own question.   I'm not sure what further discussion you were hoping for.
You have a similar civic duty to report this as you would to report other crimes.

Best Wishes.

4

Physics, Astronomy & Cosmology / Re: Is there a limit to how hot things can get?

« on: 17/05/2022 01:19:51 »

Hi.

Then you have discovered an insect that does not obey Stefan's Law,...

    I'm not sure about Steafn's law.   I'm familiar with the Stefan-Boltzmann law but I've only seen that proven for Black bodies.  There are some things that are not black bodies.

   Wikipedia uses this notation for the Stefan-Boltzmann law:
              j* = total power radiated (per unit surface area) =   ε.σ.T⁴ .     
with σ = constant;    T = temperature in kelvin     but  noteably  ε = emissivity   with  0 ≤ ε ≤ 1   and the following comment....

In the still more general (and realistic) case, the emissivity depends on the wavelength, ε = ε (λ).

   I'm not sure what wavelength they were talking about,  I guess it's the peak wavelength of the whole spectrum of emissions.  Anyway, if it is that then something approximating Wien's law implies  λ_peak ~ 1/T.   Hence, ε = ε(λ(T) )  =   a function of Temperature in disguise.
    So, all I'm asking is that  ε(T)  ~  1/T⁴    over a small range of T,   then the power radiated does lose all of it's dependence on T for that range of temperatures.

Best Wishes.

5

Chemistry / Re: How well understood is the Chemistry of the trans-uranic elements?

« on: 17/05/2022 00:49:49 »

Hi.

Thanks @Bored chemist .  It might have been more realistic to think about ligands that just offer a significant polarisation,  a  δ+  on the ligand etc.

   I agree that the main problem is (or was) finding some external factor that rivals the size of the nuclear energy changes.   As I mentioned a little earlier,  when I was a schoolchild I recall being taught that nuclear reactions are completely unaffected by any physical (or chemical) conditions external to the nucleus.  The decay of a nucleus was the textbook example of being as random a process as you will ever find in nature.
     I don't think that's on a school syllabus any longer.   At least some Nuclear reactions are not as random as we once thought.   On a side note, I wonder if Schrodinger's cat thought experiment needs to be re-written.  They usually have a radioactive substance decaying (or not decaying) as the random process determining if the poison is released.   Are there any more good examples of a process we believe to be genuinely random left in science?

Best Wishes.

6

Chemistry / Re: How well understood is the Chemistry of the trans-uranic elements?

« on: 16/05/2022 18:47:05 »

Thanks @chiralSPO .

7

Physics, Astronomy & Cosmology / Re: Is there a limit to how hot things can get?

« on: 16/05/2022 18:34:59 »

Hi.
   

The spectrum is irrelevant.

    Not if the total power emitted by the fly doesn't change at all with its temperature.   Suppose it always emits  1 W of radiation regardless of the temperature of the fly.
    There's no substance I know that does this exactly but that's why we were hypothesising.   There could be physical and chemical changes in the outer surface of the fly depending on temperature (perhaps just changing the colour of the radiating surface from black to white and keeping total power of emissions almost constant at any temperature).
- - - - - - - - -
    Anyway, I'm not going to keep standing in the way.   Keeping everything simple, the fly and thermopile can be assumed to be in thermal equilibrium.   The forum doesn't need to confuse people with complications.

Is the thermopile powered, thus allowing you to deduce the electron flow, or is it passive, thus meaning you do not know the temperature of it?

   I'm not Alancalverd but the idea seemed to be that the thermopile was powered, or somehow heated, initially to raise it to a particular temperature.   Then it is switched off and can even be disconnected from any battery or circuit.
   For the second part of the experiment you just connect a Volt meter to the thermopile.   That's the basic idea of an idealised thermopile, it's a thing that doesn't need powering by a battery, it just generates a voltage entirely due to the temperature it has.   You can measure that just by connecting a volt meter.  An ideal volt meter has an infinite resistance, so we can imagine that (almost) no electrons need to flow for that measurement.

Best Wishes.

8

Physics, Astronomy & Cosmology / Re: Is this a paradox in general relativity?

« on: 16/05/2022 02:51:37 »

Hi.

Is your origin (0,0) at the very back of the back fin of the ship like in the video?

  Yes.  The origin is intended to be exactly where they placed it in the original video (although I only sketched it, I didn't get a ruler and compass).
   The planet based observer says the back of the fin is at x= 0 when t =0.        Spaceman says the back of the fin is at x'=0 when t' =0.   

- - - - - - - - - -
   Just to emphasize one issue,  although in my diagrams it looks like the x and x' co-ordinates of the rock collision event are both  +5,   they aren't actually exactly the same.   That's just that the diagram is only a sketch and I haven't placed all the gridlines exactly the same space apart etc.   I just want to dispel the notion that there was any reason why they had to agree on the spatial location of the event... there isn't.

    I've run the precise calculation with these figures  (they are roughly what was used in the video).
Set  the velocity of the rocket =  half the speed of light.     
Use units for measuring time and distance so that the speed of light, c = 1  in those units   (Just to be clear that's not going to be seconds and metres.  It's just conventional to set c = 1).
Set the rock collision event to co-ordinates   (x, t) = ( +5.00 , +1.00 )   as was shown in my diagram for the planetary observer.
This becomes  (x', t') =  ( +5.20  ,   -1.73) in the spacemans co-ordinate system.
So, with these figures,   the spaceman and planet based observer disagree on the both the location and time of the collision event.

Best Wishes.

9

Physics, Astronomy & Cosmology / Re: Is there a limit to how hot things can get?

« on: 16/05/2022 01:30:31 »

Hi.

As @Bored chemist mentioned,    @Petrochemicals  has asked a good and challenging question, so I'm going to be on their side for a moment.

Now what do you deduce if dV/dt = 0?

   It depends on how awkward you want to be.

Simple   It shows exactly what you wanted.  The temperatures are the same.

Medium    It shows the volt meter might be broken, or similar practical problems.

Awkward    It shows the thermopile was emitting radiation at the same rate it was absorbing it.   Its temperature stays constant.  You have to be extremely careful how you get from this to deducing that the fly was at the same temperature.
   The fly was not a black body but some weird thing.   It continues radiating in much the same way, although it's temperature might be changing for a while because the radiation from the thermopile is actually heating it up, causing physical or chemical changes in the surface chitin and affecting it's emission properties.
   Obviously you can try to ensure that the fly does behave like a black body.... but you can never be sure that you have found and studied every possible way in which the fly might be transferring energy to / from the environment.   You only know that (by some mechanisms, most of which will be radiation) the fly transfers energy to the thermopile that is precisely as much energy as the thermopile emits.

Best Wishes.

10

Physics, Astronomy & Cosmology / Re: Is this a paradox in general relativity?

« on: 16/05/2022 01:03:30 »

Hi.

   I think you edited that screenshot.   It looks like you've put a blob where the rock event is and then run a thin blue line back to the spaceman's time axis.   
   You can't run that line perfectly horizontally to read off the spaceman's time value.  It has to run parallel to the spaceman's space axis.   See the diagrams I presented just earlier.

Best Wishes.

11

Just Chat! / Re: A Short puzzle with dogs.

« on: 16/05/2022 00:55:02 »

Hi.

I've always wondered whether "proper" mathematicians allowed the use of obvious symmetry and reflection as tools in a formal proof.

     At school, sure no problem.   You just had other problems to worry about, like whether an unusual proof would actually be on the mark scheme.   I mean, if there's a small error then even if the marker did spend time to examine what you tried, if it wasn't on the mark scheme and what can they do?

     At university, it depends on whether you were doing Pure Mathematics or Applied mathematics.   It general, it's OK and potentially very good - but there might be a shift in how you present the information.  In pure maths there are numerous things that are fairly obvious results when described in plain English but take undergraduates a week's coursework to set up and prove formally.   If you want to keep a Pure Mathematician busy, ask them if "this result" can be proven without Euclidean Geometry.

....that I married the only girl I ever met...

    That bit was well written.  Congratulations, it sounds amazing.

Straight to the dog house and vertically down to the river.

   I guess that might work.   The original problem did ask you to find the shortest route for a thirsty dog to get home.  The dog did get home and it was thirsty.

Best Wishes.

12

Physics, Astronomy & Cosmology / Re: Is this a paradox in general relativity?

« on: 15/05/2022 23:21:03 »

Hi.    (Also, as always... @Halc is right on his best game and submits a post just before mine.   Sorry if there's an overlap and I say something again).

    Here's the bit of the spacetime diagram we need.

ST diagram.png (21.89 kB . 1130x792 - viewed 308 times)

    The  Black axis show the time, t,  and the  space, x,  axis used by the planetary based observer.
    The Red axis, shows the time,  t'  and  space  x'  axis that the spaceman will use.
    The green line is the worldline of the nose of the rocket.
    The brown circle shows the rock collision event,  it's just a single point on the green worldline but I've made it bigger because there isn't anyway we can see just a single dot.

     Identify what you need to in that diagram before I make a mess of it and draw on some reference grid lines so that we can read off    the  (x,t) values that describe the rock collision event for the planet based observer  and also  the  (x',t') values which describe the same event in the spacemans co-ordinates.

Here's some gridlines for the (red) spaceman axis.   Slide along those gridlines and the rock collision event is at (5, -1)  for the spaceman.     It happens  at x' = 5  and   t' = -1.

ST diagram2.png (33.64 kB . 1130x792 - viewed 307 times)

Now let's clear those gridlines out of the way and put gridlines on for the planetary based observer.

ST diagram3.png (24.73 kB . 1130x792 - viewed 306 times)

The rock collision event occurred at  (x,t) = ( 5, 1),    or  x = 5,  and  t = 1    for the planetary based observer.

I hope that makes sense.... the exact placements might have been off slightly (I only sketched the diagrams not calculated them with any precision etc) but hopefully you can see how to use these diagrams and make sense of the stuff.

Best Wishes.

13

Physics, Astronomy & Cosmology / Re: Is there a limit to how hot things can get?

« on: 15/05/2022 02:30:45 »

Hi.

   Well I like @chiralSPO 's answer.

   There might be a limit to the amount of energy in the universe, so that would limit the temperature of a given bit of substance in the Universe.    (You could cheat and keep halving the amount of mass or substance and give that all the energy - but eventually you reach the situation @alancalverd described and you don't have enough particles to assign a temperature to the thing).

    I think there might be another practical limitation:  Hot things have fast moving particles.  We already know, from particle collider experiments, that if two particles collide you can create new particles.  Some of those collisions result in particles with more rest mass than the original particles (e.g. we can get a Higgs boson from what was assumed to be a collision of just two protons).   This removes kinetic energy from the system and converts to rest mass.  If you heat up a substance too much, it's likely to change into another substance (or more of the same substance) and oppose the temperature increase.  It's actually very common to describe the energies or velocities reached in particle colliders as the being the equivalent of seeing interactions that will occur at a particlular temperature -  @chiralSPO  mentioned this but didn't seem to make the connection.

Best Wishes.

14

Physics, Astronomy & Cosmology / Re: Is this a paradox in general relativity?

« on: 15/05/2022 00:26:48 »

Hi.

LATE EDITING:  @Halc got a reply in before I finished this.   I'm putting this in as it is, just because another way of looking at it might help.

   I think I can see some of what you ( @Dimensional )   are trying to say.
   If what you said were true then the collision happened at a time before t'=0 for the spaceman.   For example the collision could have happened at the spacemans time t' = -1 minute and at a location the spaceman describes as x' = -1 metre.
    This assumes the space rocket was always moving at that constant velocity,  so the time t' = -1 minute isn't anything weird,  it's just 1 minute before the spaceman set his watch to a time  t' = 0.  Similarly x' = -1 metre just means 1 metre left of the origin.

     If (because I can imagine it will be coming) the rocket was actually assumed to be stationary to start with and then quickly accelerated before holding a steady velocity throughout the rest of the motion.....   Then the diagram presented is insufficient.   All those worldlines are straight lines not curves, so no acceleration is shown.  You need a different diagram.  With the right diagram, the spaceman will find the nose of his rocket has existed at the collision event.  To say that another way, at some time and place the collision did occur for the spaceman.

   Another minor note or comment:   I'm not sure why the video showed only the time axis sloping and implied the spaceman would naturally choose to continue using the same x-axis as the planet observer.  Presumably the video presenter was trying to help and keep everything simple.   The planet observer's x axis would seem like an awkward blend of some space and time to the spaceman.   It's far better to imagine that both the spacemans axis will start to tilt away from the planet observers axis and effectively close up like a pair of scissors.



Best Wishes.

15

Physics, Astronomy & Cosmology / Re: Is this a paradox in general relativity?

« on: 14/05/2022 22:13:20 »

Hi.

It would be easier just to put the static picture on here:

   That might help.

video-snip.JPG (226.75 kB . 1815x977 - viewed 500 times)

    I think @Halc  has already answered the question correctly.
The essence of the idea is that the bump will happen, regardless of which frame of reference you use.   However, the spaceman and the planet based observer can disagree about  BOTH  where and when it happened.
    The planet based observer can call out a warning on the radio  "... Look out there's about to be a collision at our time t = 10 minutes!"   Meanwhile the spaceman will record in his log  " A minor collision happened at my time t' = 9 minutes.  By the time I received a warning it was too late AND they were wrong about the time".

Best Wishes.

16

Just Chat! / Re: A Short puzzle with dogs.

« on: 14/05/2022 19:23:03 »

Hi.

   It's probably time to discuss the solution.  I first saw this puzzle (not sure it had a dog) in a magazine produced by Imperial College, London University where the writing team had spent a little time examining the approaches used by various undergraduates of different disciplines.

One Mathematician started at #0,   most Mathematicians and Physicists started at #1,   most others tended to skip straight to #2.   Less than half the people of any discipline used #3  (they used calculus instead).

0.    Banish the infinite  A finite length route exists (e.g. one is shown in the digram with the question).  All routes we consider from now on behave sensibly.  All routes we consider have finite length between all points along the route (else it can't be the shortest route).

1.    Establish that the dog only goes to the river once   
    If it intersects the river at two (or more) points, R₁ ≠ R₂  then pick any one point, R₁.   Just draw straight lines from the start to R₁ and from there to the dog house.   That new route satisfies our criteria and cannot be longer than the old route - just by the basic definition of a straight line in Euclidean Geometry as the unique shortest path between two points.   It's possible to show that the new route is actually shorter but only a few Mathematicians bothered, most people just claimed it.  The basic proof is obvious... the dog must get back to river at R₂ so they deviated from the straight line sections somewhere.  (We did actually need step #0, if the point R on the river was infinitely far away then the dog can run along the river for a while and that's perfectly co-linear with straight line sections to the dogs home etc.)

2.   It should be clear that every finite route can be reduced to two straight line sections with three points of interest, the start (S), the point (R) on the river and the dogs home (H) at the end.   These are the only contenders for a shortest route we ever need to consider again.   Points S and H are fixed, the only issue is where you put the point R along the river.
    At this stage, over half the people (regardless of their discipline of study) continued by using calculus.  Set up a total distance function D with a single variable, x, which is the x co-ordinate of the point R along the river.   Find the local minimum.   That works.   It only finds a local minimum but you can improve on this and establish it's a global minimum just by sketching the function  etc.   (I don't think many people actually did bother).

3.   It's not necessarily "better" and it might actually take just as many lines to explain but you can, of course, solve this without calculus.

SRH.png (8.18 kB . 1130x792 - viewed 326 times)
    Just consider a related problem which is finding the shortest path from S to  H'  that crosses the river at least once.  Where H' is another dogs home located so that it is the reflection of the proper home H in a mirror along the river.  Fill in the details... Just as in the original problem it reduces to placing a point R on the river and straight line sections from S to R and from R to H'.    The total Distance D for the original problem =  SR + RH,  while the total distance for the reflected problem is SR + RH'    but  due to the triangles being identical   RH = RH'   and so these total distances are always the same.  Considering optimal solutions for either problem amounts to nothing more than varying the position of R along the river and evaluating the associated total distance D (or the identical value of D').
     Proving the existence and uniqueness of an optimum solution for the reflected problem is easy...  any path from S to H' will cross the river at least once.... so that problem reduces to find the shortest path from S to H' .   By Euclidean geometry, that's a straight line.  ∴ R can only be placed at one point on the river for an optimal solution to the reflected problem.
    That's it,  dot the i and cross the t .   The existence and uniqueness of an optimal solution for the original problem follows.
   Simple geometry will then tell you where R must be placed,   @Halc  said ~43m west of the house,  @Colin2B  said to use the angle of incidence = angle of reflection.   Well done to those two and especially for spotting that reflection would help instead of going straight for the calculus.

- - - - - - - - - - -
    If you were developing these ideas, you could have the dog go for a swim in the river and be slower when wet.  To solve these problems you need a woofraction index, a ratio of speeds while wet and dry.

Best Wishes.

17

New Theories / Re: what is temperature?

« on: 14/05/2022 14:13:02 »

Hi.

   This thread has got quite unpleasant, hasn't it?  It's not my forum and there's no reason my opinion is worth writing down or reading.   However, I don't think I'll be following this thread anymore.  My apologies if I don't reply to someone who has quoted or tagged me  ( @Eternal Student )   etc.

Best Wishes.
   

18

New Theories / Re: what is temperature?

« on: 14/05/2022 02:19:54 »

Hi.

    Thanks for your comments @alancalverd .   

They don't need to be identical. Porridge is inhomogeneous, but Goldilocks was able to measure its temperature. Temperature is the mean kinetic energy of all the particles in a sample.

    The original statement(s) I made (pages back, for example post #278) concerns the modern definition of temperature in kelvin since May 2019.  In the models they use for that theoretical temperature scale,  all the particles of one species are assumed to be identical to each other (apart from having their own velocity which follows a Boltzmann distribution).   There's just no way I could have all the i dotted and all the t crossed.

      Kinetic theory provides a microscopic account of temperature for some bodies of material, especially gases, based on macroscopic systems' being composed of many microscopic particles, such as molecules and ions of various species, the particles of a species being all alike.

https://en.wikipedia.org/wiki/Temperature#Kinetic_theory_of_gases

     Anyway, the particles of a species in the porridge are identical (in the model) but the porridge can have more than one species of particle.   
- - - - - - - - - -

The first bowl was <unknown>,  the second bowl was <unknown>  but the last was just <unknown>

   As it happens I don't think there is a good theoretical model for porridge.  As such Goldilocks probably can't determine the temperature of her porridge on the modern (post 2019) kelvin scale.   That temperature is simply "unknown" or "undetermined" at this time.
     ....In an ideal gas, and in other theoretically understood bodies, the Kelvin temperature is defined to be proportional to the average kinetic energy of non-interactively moving microscopic particles, which can be measured by suitable techniques....     [ https://en.wikipedia.org/wiki/Temperature#Theoretical_scales ]
      ... making the clear implication that if the porridge is not theoretically understood,  specifically that we don't have a good model for it right now, then  .... who knows,  best not give it a temperature in kelvin (kelvin post 2019)....
   
    It would be worth me saying this again:  The very latest entirely theoretical approach to defining temperature came in from May 2019 and Wikipedia articles on temperature are getting edited every week trying to bring them inline with these changes.   I'm not claiming to be an expert on the new approach.   

Best Wishes.

19

Plant Sciences, Zoology & Evolution / Re: Which is the best animal has the best senses?

« on: 14/05/2022 00:07:36 »

Hi.

   It is an interesting question and thanks for submitting it.

   Regrettably I think it would take too much space here to list everything and all the contenders for animals with "the best senses".

    There's reasonable information in this article:
https://www.sciencefocus.com/nature/amazing-animal-super-senses/
    There's also hours of popular science videos about animals and their amazing senses.   This series was quite good, if you can still get hold of it  (I'm sorry but free access has timed out from this link):
https://www.bbc.co.uk/programmes/b04fhp70       "Super Senses:  The secret power of animals" by the BBC.

   There is endless amounts of information.

   Exactly as you stated,  there is considerable variation in sensory capabilities between species.    So it's not as simple as saying   "which species has the best sense of smell?",   some species are generally very good at odour detection,  e.g.  dogs,  but they can be quite oblivious or unaware of one type of molecule.   That might be a molecule that some other species uses as an important odour marker and that other species might be extremely sensitive to.   As such our presumed best overall sniffer  (the dog) is effectively "blind" to one odour that someone in the animal kingdom thinks is very important.    We also have a problem if we take one animal out of its natural environment and put them in some other.   For example, a dog can't smell very much at all when they are in water but a shark is a completely different thing and can smell blood in the water from a quarter-mile.

    I notice that you have been extremely precise and tried to specify some criteria you would use to determine which animal was overall "the best"...

...based on density, sensitivity and variety of receptors?

    However, even that is still difficult to answer.   How much importance do you want to put on each of those things?   For example, is the ability to detect electric fields so amazing that having that ability tops the score for "variety of receptors"?

    It's usually said that every animal is well adapted and it is often the very best it can be for the niche it occupies in the overall ecology.   It doesn't matter if its senses seem unimportant to another animal, they are important for this animal in this niche.

Best Wishes.

20

Just Chat! / Re: A Short puzzle with dogs.

« on: 13/05/2022 23:34:08 »

Hi @Rolerwill ,

    I'm not sure I've spoken to you before.  Welcome to the forum.
I think you might be talking about the first ever puzzle discussed on this thread.    There are some answers already presented for that.   It's also just an idealised problem and in real life things would get in the way.   If you're interested, the discussion and solutions presented by the Guardian newspaper will probably save time rather than reading through the whole of this thread. 
   https://www.theguardian.com/science/2019/jun/03/can-you-solve-it-dogs-in-pursuit  .

Best Wishes.