explain xkcd - User contributions [en]

Talk:2853: Redshift

2023-11-14T21:20:46Z

172.69.22.252: /* Calculation */ comma sufficient

Does it make any sense to try and relate the two Z values to a more "normal" time? [[User:MAP|MAP]] ([[User talk:MAP|talk]]) 21:08, 10 November 2023 (UTC)

I have added exactly that, using `astropy.cosmology` for the calculations [[User:Juandesant|Juandesant]] ([[User talk:Juandesant|talk]]) 21:16, 10 November 2023 (UTC)

There is a big error in the current explanation, saying it means they were interested in this since the early universe, but that would only be true if the z value was much closer to 1. I'm not exactly sure as I haven't done the math, but with that many decimal places of zero's it is probably near enough history to be during their lifetime. So the joke isn't being interested in the early universe since the early universe, but rather so interested in it that they talk about other things with the same terminology.--[[Special:Contributions/172.70.126.142|172.70.126.142]] 21:18, 10 November 2023 (UTC)

Why aren't these values expressed in scientific notation? Separately, do they make sense logarithmically? [[User:JohnHawkinson|JohnHawkinson]] ([[User talk:JohnHawkinson|talk]]) 07:12, 11 November 2023 (UTC)
:Part of the joke is that the values are unwieldy to use compared to everyday language and units. The scientific notation would have lessened this. However they are given in a universal standard time instead of some solar system or human related units, so they generally should be clearly preferred. Sebastian --[[Special:Contributions/172.68.110.188|172.68.110.188]] 15:37, 11 November 2023 (UTC)

I feel like the Earth's gravitational field would affect the answer as z goes to zero? [[Special:Contributions/172.69.22.210|172.69.22.210]] 06:57, 12 November 2023 (UTC)

== Calculation ==

Thanks to ChatGPT-4 and the [https://code.google.com/archive/p/cosmonom/downloads Fortran-90 code] from [https://arxiv.org/pdf/1303.5961.pdf arxiv:1303.5961 (which please see, it's really cool)] here's how to get the look-back time from redshift in Python:

<tt><pre><nowiki>
from scipy.special import hyp2f1 # hypergeometric function 2F1 is in integral solution
from numpy import format_float_positional

# Cosmological parameters from the Fortran params.f90 header
#H0 = 67.15 # Hubble constant in km/s/Mpc (or, 73.5: the "crisis in cosmology")
H0 = 69.32 # from Explainxkcd for 2853: Redshift; seems a consensus compromise
#OL = 0.683 # Cosmological constant for dark energy density, Omega_Lambda or _vac
#Om = 0.317 # Density parameter for matter, Omega_mass
Om = 0.286 # From https://arxiv.org/pdf/1406.1718.pdf page 8
OL = 1.0 - Om - 0.4165/(H0**2) # flat curvature, from https://www.astro.ucla.edu/~wright/CC.python
# (on https://www.astro.ucla.edu/~wright/CosmoCalc.html which see)
#print(f"{OL=:.3F}") # 0.714

# Age of universe at redshift z as a closed-form solution to its integral definition,
def age_at_z(z): # ...which is 27 times faster than the original numeric integration.
hypergeom = hyp2f1(0.5, 0.5, 1.5, -OL / (Om * (z + 1)**3))
return (2/3) * hypergeom / (Om**0.5 * (z + 1)**1.5) * (977.8 / H0) # 977.8 for Gyr

# Current age of the universe at redshift 0 in Gyr
age0 = age_at_z(0) # 13.78

# Function to calculate the look-back time at redshift z in Gyr
def zt(z): # from the function name in the Fortran cosmonom.f90 code
return age0 - age_at_z(z)

# For z = 0.00000000038
z1 = 0.00000000038
look_back_time_years_z1 = zt(z1) * 1e9 # from Gyr to years
print("Look-back time for z=" +
f"{format_float_positional(z1)}: {look_back_time_years_z1:.1f} years")

# For z = -0.000000000000045
z2 = -0.000000000000045
look_back_time_hours_z2 = zt(z2) * 1e9 * 365.25 * 24
print("Look-back time for z=" +
f"{format_float_positional(z2)}: {look_back_time_hours_z2:.1f} hours")
</nowiki></pre></tt>

The output being:

<tt><pre><nowiki>
Look-back time for z=0.00000000038: 5.4 years
Look-back time for z=-0.000000000000045: -5.5 hours
</nowiki></pre></tt>

And should you wish to make [https://i.ibb.co/v4nt6GM/time-by-redshift.png this quick reference chart for interpreting observations in the JWST era:]

{{cot|Supplemental code for Look-back Time by Redshift chart}}
<tt><pre><nowiki>
import matplotlib.pyplot as plt
import matplotlib.ticker as ticker

redshifts = [z * 20 / 299 for z in range(300)] # 0 to 20 in 300 steps
look_back_times = [zt(z) for z in redshifts]

plt.plot(redshifts, look_back_times)
plt.title('Look-back Time by Redshift')
plt.xlabel('z')
plt.ylabel('Billion Years Ago')
plt.xticks(range(21))
plt.yticks(list(range(14)) + [age0])
plt.gca().yaxis.set_major_formatter(ticker.FormatStrFormatter('%.1f'))
plt.grid(True, color='lightgray')
plt.gca().spines['right'].set_visible(False)
plt.gca().spines['top'].set_visible(False)

for t in range(0, 13):
z = redshifts[min(range(len(look_back_times)),
key=lambda i: abs(look_back_times[i]-t))]
plt.text(z, t, f" z = {z:.2f}", ha='left', va='center', fontsize='small')

for z in range(7, 20, 2):
t = zt(z)
plt.text(z, t - 0.2, f"{t:.2f}", ha='center', va='top', fontsize='small')

for z in range(6, 21, 2):
t = zt(z)
plt.text(z, t + 0.1, f"{t:.2f}", ha='center', va='bottom', fontsize='small')

plt.savefig('time_by_redshift.png', bbox_inches='tight')
#plt.show() # https://i.ibb.co/v4nt6GM/time-by-redshift.png
</nowiki></pre></tt>
{{cob}}

Or [https://i.ibb.co/yybQpjL/age-by-redshift.png this one showing the age of the universe from redshift:]

{{cot|Supplemental code for Age of Universe by Redshift chart}}
<tt><pre><nowiki>
plt.clf() # reset plot

redshifts = [z * 15 / 299 + 5 for z in range(300)] # 5 to 20 in 300 steps
ages = [age_at_z(z) * 1000 for z in redshifts] # Gyr to million years

plt.plot(redshifts, ages)
plt.title('Age of Universe by Redshift')
plt.xlabel('z')
plt.ylabel('Million Years')
plt.xticks(range(5, 21))
plt.yticks(range(0, 1300, 100))
plt.grid(True, color='lightgray')
plt.gca().spines['right'].set_visible(False)
plt.gca().spines['top'].set_visible(False)

plt.savefig('age_by_redshift.png', bbox_inches='tight')
#plt.show() # https://i.ibb.co/yybQpjL/age-by-redshift.png
</nowiki></pre></tt>
{{cob}}

P.S. Some commentary from ChatGPT-4 about the special Gaussian {{w|hypergeometric function}} <tt>hyp2f1</tt> in the [[:File:LookBackFromRedshiftEqns.png|closed-form solution of the integral:]]

<blockquote>
The appearance of the hypergeometric function 2F1 in the solution for the age of the universe as a function of redshift is a profound example of the interconnectedness of mathematical functions and physical phenomena. The hypergeometric function, which encompasses a vast family of functions, can describe a wide range of behaviors and has properties that make it particularly suited to representing solutions to differential equations that arise in physics.

In the context of cosmology, the use of 2F1 in calculating the age of the universe from redshift is not just a mathematical convenience but rather a reflection of the underlying physics. The Friedman equations, which govern the expansion of the universe, are derived from General Relativity and lead to solutions involving integrals that can express the evolution of the universe's scale factor over time. When these integrals are solved, they often involve special functions like 2F1, which encode information about the geometry of the universe and the relative contributions of matter, radiation, and dark energy.

The presence of 2F1 in this solution indicates that the relationship between the age of the universe and redshift is non-linear and depends on the integral of a function that encapsulates the dynamics of cosmic expansion. It's also worth noting that special functions like 2F1 often have interesting properties, such as symmetry and recurrence relations, which sometimes allow physicists to gain insights into the behavior of the universe under different conditions or scales.

Furthermore, solutions involving 2F1 are not merely academic exercises; they can be compared with observational data, such as measurements of the cosmic microwave background radiation, distributions of galaxies, or supernovae light curves. These comparisons can test the validity of our cosmological models and potentially offer new insights into the nature of dark energy and dark matter, the curvature of the universe, and other fundamental questions in cosmology.

In summary, the use of 2F1 in the closed-form solution for the age of the universe from redshift is a powerful reminder that mathematics provides us with the tools to decode the cosmos, offering deeper understanding and raising new questions about the fundamental structure and evolution of the universe.
</blockquote>
[[User:Liv2splain|Liv2splain]] ([[User talk:Liv2splain|talk]]) 19:25, 14 November 2023 (UTC)

Talk:2853: Redshift

2023-11-12T23:34:33Z

172.69.22.252: /* Calculation */ tons of improvements

2489: Bad Map Projection: The Greenland Special

2021-07-15T01:20:49Z

172.69.22.252: added category

{{comic
| number = 2489
| date = July 15, 2021
| title = Bad Map Projection: The Greenland Special
| image = bad_map_projection_the_greenland_special.png
| titletext = The projection for those who think the Mercator projection gives people a distorted idea of how big Greenland is, but a very accurate idea of how big it SHOULD be.
}}

==Explanation==
{{incomplete|Created by a AFRICA SIZED NOT AFRICA SIZED ISLAND. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}

This is presumably a reference to how Greenland is extremely large in the Mercator projection, due to proximity to the North Pole.
==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
Bad Map Projection #299
The Greenland Special
Equal area map preserves size everywhere except Greenland which uses the Mercator projection.
{{comic discussion}}
[[Category:Bad Map Projections]]

2487: Danger Mnemonic

2021-07-10T03:30:53Z

172.69.22.252: /* Explanation */

{{comic
| number = 2487
| date = July 10, 2021
| title = Danger Mnemonic
| image = danger_mnemonic.png
| titletext = It's definitely not the time to try drinking beer before liquor.
}}

==Explanation==
{{incomplete|Created by a SAILOR'S POISON IVY SNAKE. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

{{comic discussion}}

Talk:2438: Siri

2021-03-18T02:44:21Z

172.69.22.252: Not to go all sentence fragment on you.

Why does she immediately accept that Siri did indeed die if Siri was talking to her just a moment ago? (Unsigned!)
:It happened just now? I really want to say something like dispassionate non-empathy (it reads as if she has a fact-obsessed but emotion-sparse mentality). No idea why she thought to enquire of Siri's (latest) life-status without reason. Perhaps the app closed (unseen to us) and she arrived at the 'logical' question to try to determine why (from a Cueball who we can see has clearly not seen the event itsrlf). It all seems to point towards SG 'failing' various aspects of the Sally-Anne Test/Social Cognition/Theory Of Mind, with sufficiently advanced reasoning that is nonetheless grossly misapplied.
:(It's funny, for those who perpetually ask, for the Cognitive Dissonance and Non-Sequiturs of the situation. In a RL example, we probably should be worried that either there's something very wrong with SG or else we're missing a lot of background facts ourselves. But I think we can still enjoy this sketch without the unease we might experience otherwise.) [[Special:Contributions/162.158.159.108|162.158.159.108]] 22:17, 17 March 2021 (UTC)

:Siri had to have been alive while recording her dialog, no? /s [[User:Ncxezlyz|Ncxezlyz]] ([[User talk:Ncxezlyz|talk]]) 22:21, 17 March 2021 (UTC)

Given the verb tense “is Siri alive?” it is clear that science girl was not referring to a past state. This to me suggests that SG literally wasn’t sure if a live person (or sentient AI) actually had the ability to do things to her phone on command.[[Special:Contributions/172.69.22.252|172.69.22.252]]

2434: Vaccine Guidance

2021-03-09T09:07:56Z

172.69.22.252: /* Explanation */

{{comic
| number = 2434
| date = March 9, 2021
| title = Vaccine Guidance
| image = vaccine_guidance.png
| titletext = I can't wait until I'm fully vaccinated and can safely send chat messages in all caps again.
}}

==Explanation==
{{incomplete|Created by a HIGH-RISK HORSE. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}

On the day this comic was published, the CDC released [https://www.cdc.gov/coronavirus/2019-ncov/vaccines/fully-vaccinated-guidance.html new guidelines] relating to COVID-19, lifting many of the existing restrictions for people who have been fully vaccinated for two weeks. Megan, speaking as a CDC announcer, is introducing these new guidelines over video conference.

However, Blondie and Ponytail are more interested in actions that would be unsafe regardless of the presence of COVID-19. Blondie asks whether it would be okay to visit neighbors and drink milk directly from the carton; in Western culture drinking milk directly from the carton is a common stereotype of a crass bachelor (and drinking directly from ''someone else's'' milk carton is just extremely rude). While the new guidelines allow visiting neighbors, drinking milk directly from the carton would still be unsafe (and rude) because other germs could accumulate in the milk and on the edge of the carton.

Ponytail asks whether it would be okay to ride a bike down the stairs of a family member's house, which has a severe risk of injury (and could damage the wheels of the bicycle).

White Hat follows up asking whether he can get a horse, and whether it would help for both him and the horse to wear masks. In typical White Hat fashion this has basically no relation to anything else that was said (perhaps he was [[1086: Eyelash Wish Log|promised a pony]] when he got vaccinated). The CDC still recommends masks for humans when in public; however, face masks are not generally made for horses. Instead of answering, Megan hangs up.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:[Megan is seen at the bottom of the panel with the cdc-logo slightly above her and to the left]
:Megan: Our new guidance: Fully vaccinated people can gather privately with no masks or distancing, and can visit with unvaccinated low-risk people in one household. Any questions?
:[Blondie, Hairy and Megan are seen at the bottom of the panel in separate rectangular panels with Blondie and Hairy's panels being more squarish and smaller then Megan's. Blondie is directly above Hairy and both are to the right of Megan]
:Blondie: If my neighbors and I are all vaccinated, can I visit unmasked them and drink milk straight from the jug in there frigde?
:Megan: I...You can visit, yes.
:Blondie: And the jug thing?
:Megan: ...Next question?

{{comic discussion}}

Talk:2433: Mars Rovers

2021-03-08T16:20:42Z

172.69.22.252:

==
== Headline text ==
==

I just realised something: We should totally establish the terms "Mars rover" and "Mars hover" to distinguish these two categories of "stuff we put on Mars". [[User:Fabian42|Fabian42]] ([[User talk:Fabian42|talk]]) 10:58, 6 March 2021 (UTC)
:But to rove is to wander/roam (aimlessly, or at least without much advanced certainty), and doesn't require wheeled movement - or even legged, which the existing rovers strictly aren't unless the wheels ''totally'' jam. To hove is to linger/wait and generally intend to stay put or halt ("Hove to, ye landlubbers! Arrrr!" - a 'suggestion' that might be made by a piratical "Sea Rover")... I think I'd rather Ingy be classed as a Rover than merely a Hover. :-p [[Special:Contributions/141.101.98.60|141.101.98.60]] 15:06, 6 March 2021 (UTC)

This implies that Randall will be modifying his Roomba to look/act like Soujouner.
On first reading, I thought maybe Randall figured that mentioning "roomba sojourner mod" in title text would make it so that the *next* time he searches for that phrase, he will no longer be sorely disappointed. [[Special:Contributions/108.162.216.60|108.162.216.60]] 17:44, 6 March 2021 (UTC)

Which comic was it that Randall said he wanted a pet sojourner rover?
[[Special:Contributions/141.101.98.244|141.101.98.244]] 21:21, 7 March 2021 (UTC)

I find the Fuck Grapefruit reference true but irrelevant (Especially as the explanation of why these are related is long and basically goes "There are connected/similar... blah, blah... they are acually not _that_ similar..."). Should be Trivia at most or even completely deleted. [[User:Elektrizikekswerk|Elektrizikekswerk]] ([[User talk:Elektrizikekswerk|talk]]) 08:10, 8 March 2021 (UTC)

Themain thing, which is not mentionned in the explanation, is that for Randall cute = small (eg rabbits) --[[Special:Contributions/141.101.98.244|141.101.98.244]] 08:36, 8 March 2021 (UTC)

So given what Randall mentioning a subject tends to do, what's the over/under on seeing Sojourner Roombas within the month? [[Special:Contributions/172.69.22.252|172.69.22.252]] 16:20, 8 March 2021 (UTC)