Note: this is a work in progress. Feel free to make additions, improvements or edits but be aware that they may be removed or undone.
¶ Basic Concepts
Think of the Order of the Sun as having 4 distinct levels:
- Faith, the resource called "faith"
- Worship, converted from faith by praising the sun \o/
- Epiphany, converted from worship by adoring the stars
- Transcendence
Every level improves the one before it:
- 4 -> 3: A higher transcendence tier (TT) means you get more epiphany for your worship whenever you adore the stars
- 3 -> 2: More epiphany means you get more worship whenever you praise the sun \o/
- 2 -> 1: More worship means you will generate faith more rapidly (assuming you have Solar Revolution)
The fact that each level improves the one before it means that you should ALWAYS go from the higher level first, ie transcend -> faith reset -> praise the sun \o/
*Go from the top down, TAP: Transcend, Adore the galaxy, Praise the sun \o/ (Fun fact: Bloodrizer specifically picked the verb "Adore" to preserve the TAP acronym!)
This was a lot more confusing before 1.4.8.1, when worship was called "total faith" and epiphany wasn't named at all.
¶ Flowchart
¶ When Should I Praise?
You can pretty much Praise the Sun whenever you want after buying Solar Revolution. Praising the sun will consume all your faith and increase your Solar Revolution production bonus. The Solar Revolution bonus is soft-capped. Early in the game (the first few runs) you may not be able to reach the cap. A few runs later, you may need to fill your faith and Praise the Sun many times to reach the cap. Later in the game you can reach the Solar Revolution cap by filling your faith and praising once.
You won't want to Praise when you are saving up your faith to buy Religion upgrades, or when you are trying to cap your faith so that you can Transcend or Adore.
¶ When Should I Adore?
You can always Adore just before you reset; the game will Adore for you if you don't, and you get a small 1% bonus if you remember to click on the button.
Otherwise, Adoring will remove your Solar Revolution bonus, and you can Adore and then Praise whenever you have enough faith to restore your Solar Revolution bonus back close to its cap.
¶ When Should I Transcend?
Each transcend level costs a certain amount of your Praise Bonus as given in the table below. In the first few runs, when you can't reach your Solar Revolution cap, after you Transcend, you will immediately Adore. (And if you aren't about to reset, you will then Praise.) You want the Adore to restore your Praise Bonus. So you will need enough Worship, as give in the tables below, so that your Praise Bonus will be restored.
Once you can cap (or nearly cap) your Solar Revolution bonus by Praising your capped faith once, it's no longer useful to build up a large pool of Worship. Instead, the equivalent strategy is to Transcend after raising your Praise Bonus to 2x the level needed to Transcend. (The tables below suggest there are more optimal strategies. For example, when you have Black Obelisks, Transcending will increase your Solar Revolution cap allowing you to gain faith faster, so transcending sooner can be beneficial.)
¶ How to do Mid-Run Transcendence
- If you can't quickly cap your Solar Revolution bonus, generate a big worship pool (see the second table below).
- If you can quickly cap your Solar Revolution bonus, get 1.5-2 times the required Praise Bonus for the next tier (table below)
- Cap faith
- Go from the top down, TAP: Transcend, Adore the galaxy, Praise the sun \o/ (Fun fact: Bloodrizer specifically picked the verb "Adore" to preserve the TAP acronym!)
Note: you should probably clone your game and do some tests to ensure that you can get your SR back to where it was fairly quickly after doing your faith resets
| Transcendence Tier | Minimum Praise bonus % needed | 1.5 x Praise bonus | 2 x Praise bonus | Break-even Praise bonus (0 Black Obelisks) | Break-even Praise bonus (10 Black Obelisks) | Break-even Praise bonus (50 Black Obelisks) | Break-even Praise bonus (many Black Obelisks) |
|---|---|---|---|---|---|---|---|
| Tier 1 | ~1.97% | ~2.95% | ~3.94% | ~2.08% | |||
| Tier 2 | ~5.90% | ~8.86% | ~11.81% | ~6.92% | |||
| Tier 3 | ~17.38% | ~26.07% | ~34.76% | ~21.85% | |||
| Tier 4 | ~49.29% | ~73.94% | ~98.58% | ~65.54% | |||
| Tier 5 | ~136.45% | ~204.68% | ~272.90% | ~191.53% | ~184.73% | ||
| Tier 6 | ~373.55% | ~560.33% | ~747.11% | ~552.99% | ~529.83% | ||
| Tier 7 | ~1.02K% | ~1.53K% | ~2.04K% | ~1.59K% | ~1.51K% | ||
| Tier 8 | ~2.77K% | ~4.16K% | ~5.54K% | ~4.52K% | ~4.28K% | ||
| Tier 9 | ~7.53K% | ~11.30K% | ~15.07K% | ~12.85K% | ~12.09K% | ||
| Tier 10 | ~20.48K% | ~30.72K% | ~40.96K% | ~36.38K% | ~34.05K% | ~31.95K% | ~30.64K% |
| Tier 11 | ~55.67K% | ~83.51K% | ~111.35K% | ~102.69K% | ~95.66K% | ~89.74K% | ~86.27K% |
| Tier 12 | ~151.34K% | ~227.01K% | ~302.68K% | ~289.14K% | ~268.11K% | ~251.58K% | ~242.36K% |
| Tier 13 | ~411.39K% | ~617.08K% | ~822.77K% | ~812.23K% | ~749.95K% | ~704.05K% | ~679.53K% |
| Tier 14 | ~1.12M% | ~1.68M% | ~2.24M% | ~2.28M% | ~2.09M% | ~1.97M% | ~1.90M% |
| Tier 15 | ~3.04M% | ~4.56M% | ~6.08M% | ~6.37M% | ~5.84M% | ~5.49M% | ~5.32M% |
| Tier 16 | ~8.26M% | ~12.39M% | ~16.53M% | ~17.81M% | ~16.26M% | ~15.30M% | ~14.83M% |
| Tier 17 | ~22.46M% | ~33.69M% | ~44.92M% | ~49.68M% | ~45.21M% | ~42.57M% | ~41.34M% |
| Tier 18 | ~61.06M% | ~91.58M% | ~122.11M% | ~138.45M% | ~125.60M% | ~118.37M% | ~115.08M% |
| Tier 19 | ~165.97M% | ~248.95M% | ~331.93M% | ~385.35M% | ~348.55M% | ~328.80M% | ~320.01M% |
| Tier 20 | ~451.14M% | ~676.71M% | ~902.28M% | ~1.07G% | ~966.42M% | ~912.51M% | ~889.03M% |
| Tier 21 | ~1.23G% | ~1.84G% | ~2.45G% | ~2.68G% | ~2.53G% | ~2.47G% | |
| Tier 22 | ~3.33G% | ~5.00G% | ~6.67G% | ~7.41G% | ~7.01G% | ~6.84G% | |
| Tier 23 | ~9.06G% | ~13.59G% | ~18.12G% | ~20.50G% | ~19.41G% | ~18.97G% | |
| Tier 24 | ~24.63G% | ~36.95G% | ~49.26G% | ~56.68G% | ~53.72G% | ~52.52G% | |
| Tier 25 | ~66.96G% | ~100.43G% | ~133.91G% | ~156.62G% | ~148.56G% | ~145.35G% | |
| Tier 26 | ~182.00G% | ~273.01G% | ~364.01G% | ~410.59G% | ~401.99G% | ||
| Tier 27 | ~494.74G% | ~742.11G% | ~989.48G% | ~1.13T% | ~1.11T% | ||
| Tier 28 | ~1.34T% | ~2.02T% | ~2.69T% | ~3.13T% | ~3.07T% | ||
| Tier 29 | ~3.66T% | ~5.48T% | ~7.31T% | ~8.64T% | ~8.48T% | ||
| Tier 30 | ~9.94T% | ~14.91T% | ~19.87T% | ~23.84T% | ~23.39T% |
- Break-even means that Solar Revolution cap * (1 + Praise bonus) * Adore multiplier is the same before and after transcending.
- Black Obelisks include phantom Black Obelisks from Atheism challenges.
| To Transcendence Tier | Minimum Praise Bonus % needed | Worship needed to restore Praise Bonus |
|---|---|---|
| Tier 1 | ~1.97% | ~ 2950 |
| Tier 2 | ~5.90% | ~ 5220 |
| Tier 3 | ~17.38% | ~ 14.9 K |
| Tier 4 | ~49.29% | ~ 58.4 K |
| Tier 5 | ~136.45% | ~277 K |
| Tier 6 | ~373.55% | ~ 1.46M |
| Tier 7 | ~1.02K% | ~ 8.17M |
| Tier 8 | ~2.77K% | ~ 47.5 M |
| Tier 9 | ~7.53K% | ~284 M |
| Tier 10 | ~20.48K% | ~ 1.73G |
| Tier 11 | ~55.67K% | ~ 10.7 G |
| Tier 12 | ~151.34K% | ~ 67.6 G |
| Tier 13 | ~411.39K% | ~431 G |
| Tier 14 | ~1.12M% | ~ 2.77T |
| Tier 15 | ~3.04M% | ~ 18.0 T |
| Tier 16 | ~8.26M% | ~118 T |
| Tier 17 | ~22.46M% | ~776 T |
| Tier 18 | ~61.06M% | ~ 5.14P |
| Tier 19 | ~165.97M% | ~ 34.3 P |
| Tier 20 | ~451.14M% | ~230 P |
| Tier 21 | ~1.23G% | ~ 1.55E |
| Tier 22 | ~3.33G% | ~ 10.5 E |
| Tier 23 | ~9.06G% | ~ 70.9 E |
| Tier 24 | ~24.63G% | ~483 E |
| Tier 25 | ~66.96G% | ~ 3.30Z |
| Tier 26 | ~182.00G% | ~ 22.6 Z |
| Tier 27 | ~494.74G% | ~155 Z |
| Tier 28 | ~1.34T% | ~ 1.07Y |
| Tier 29 | ~3.66T% | ~ 7.38Y |
| Tier 30 | ~9.94T% | ~ 51.1 Y |
The remainder of this page discusses implementation details and the math used to derive these tables.
¶ How the Code Works
Functions and variables:
- TVR(value) =
(sqrt(1+80*value)-1)/20 - bonusRatio =
(1+TT)^2- bonusRatio is multiplied by 1.01 for manual adoration (as opposed to the automatic adoration which happens when you reset your game)
Prior to 1.4.8.1, epiphany was actually stored as a hidden resource, colloquially known as 'apocrypha points'. It still works the same, but it's a lot clearer now.
How epiphany is calculated:
- When you adore the stars, epiphany added =
(worship / 1000000) * bonusRatio - When you transcend, epiphany is removed; total cost of all your transcendence tiers = (((eTT/5+1)2)-1)/80
- Total epiphany =
sum of faith resets - (((e^TT)/5+1)^2-1)/80 - Your praise bonus = TVR(epiphany)
- The TVR function calculates your Praise Bonus as a decimal; multiply by 100 to get the percentage bonus displayed.
¶ How the Code Works II
This is the math behind the Transcend from Worship table above. This mostly restates How the Code Works above, but in somewhat different words. For those who really want to dig into the math, having two slightly different wordings to compare might help understand some of the details better. If you don't really care about the math, you should skip this.
Faith is displayed along with other visible resources. By clicking on the gear icon for resources, one can get a "show hidden resources" checkbox. Clicking on that will cause Worship and Epiphany to be displayed.
Clicking on "Praise the Sun" in the Religion tab will convert Faith to Worship.
- The "Praise the Sun" button displays a "Praise Bonus".
- How the Code Works tells us the Praise Bonus is computed from Epiphany as
(sqrt(1+80*epiphany)-1)*5 - Worship will be increased by:
faith * (1 + (sqrt(1+80*epiphany)-1) / 20) - For example, I have 9,690 Epiphany. If I Praise the Sun, my Worship will increase by about 45 times my Faith.
- (For large values of Epiphany, Worship increases by approximately:
faith * 0.45 * sqrt(epiphany).)
Clicking on "Adore the Galaxy" will convert Worship to Epiphany.
- The "Adore the Sun" button displays a conversion multiplier. This multiplier is called the "bonusRatio" above. The displayed value is simply:
(1 + TT)^2where TT is the current Transcendence Tier. - Epiphany generated =
(worship / 1000000) * (1 + TT)^2 - If the button is manually clicked, then there is a 1% bonus.
- Example: I'm currently at Transcendence Tier 8 and have ~374M Worship. So I would gain 374 * 81 ≈ 30,000 Epiphany.
Clicking on the Transcend button will spend Epiphany to raise my Transcendence Tier.
- The epiphany cost to transcend from level TT is
((e^(2*TT+2))/10 + e^(TT+1) - (e^(2*TT))/10 - e^(TT)) / 200 - For high TT, this is approximately
e^(2*TT) * (e^2 - 1) / 2000 - Example: to get to Tier 9, I expect to spend a little more than 28K Epiphany.
I'd expect that whenever we transcend, we want at least enough Worship so that we can restore our Praise Bonus.
If we transcend mid-tier, since Solar Revolution is capped, it seems like we can restore most of our Solar Revolution bonus reasonably quickly.
To replace spent Epiphany with Worship when transcending from level TT, we need
- epiphany from worship > transcendence cost
- ≈
worship / 1000000 * (2 + TT)^2 > (2.718^(2*TT)) * 0.003194 - =
worship > (2.718^(2*TT)) * 3194 / (2 + TT)^2 - Example: At my current Tier of 8, I need
(2.718^16)*3194/100or somewhere over 283M worship.
Experimental work in progress:
What we must want to optimize is the rate of generation of epiphany (or Praise bonus) while maintaining a high Solar Revolution bonus. Epiphany is generated as roughly worship*TT^2. Where worship is generated as roughly faith*sqrt(epiphany). A nice circular generation function. E' = F*sqrt(E)*TT^2. And the rate of increase in F depends on the Solar Revolution cap which is a function of TT*obelisks. E' = TT*obelisks*sqrt(E)*TT^2. To keep the rate of generation constant across a Transcend, obelisks shouldn't be important; that should just be a constant multiplier before and after. Say we will spend S epiphany, and before we transcend we have some multiple k of that amount, then we want
TT^3*sqrt(k*S) <= (TT+1)^3 * sqrt((k-1)*s)- ⇒
sqrt(k/(k-1)) <= ((TT+1)/TT)^3 - ⇒
k/(k-1) <= ((TT+1)/TT)^6 - ⇒
k <= c * (k-1) - ⇒
k <= ck - c - ⇒
c <= (c-1)*k - ⇒
c/(c-1) <= k - ⇒
(c-1)/c >= 1/k - ⇒
1 - 1/c >= 1/k - ∴
1/k <= 1 - (TT/(TT+1))^6
The above equation is only used when there are some obelisks.
This suggests waiting longer before transcending. For example, when transcending from level 20, the TT-cubed bonuses will increase production by about 30%. Implying should reduce the Praise Bonus only by about 30% and not cut it in half as is suggested by the tables.
A more accurate equation than the above is
E'=TT*sqrt(E)*(TT+1)^2- ⇒
TT*sqrt(k*S)*(TT+1)^2 <= (TT+1)*sqrt((k-1)*S)*(TT+2)^2 - ⇒
sqrt(k/(k-1)) <= (TT+1)*(TT+2)*(TT+2)/(TT*(TT+1)*(TT+1)) - ∴
k/k-1 <= ((TT+2)^2)/(TT*(TT+1))
That doesn't give hugely different results.
¶ Simple & rough calculations
This little snippet compiles the most basic explanations of relations between faith, worship, epiphany and Transcendence Tiers.
It's given as a tool for doing quick & approximate calculations without the need to dive into actual "big" maths behind the scenes. Use it as a quick reference if you want to decide for yourself if e.g. Transcending is worth it or not (that's what I created this for and it works great for me so I decided to share it).
All errors are generally < 3% overestimations and work best for >100k worship and >5 epiphany (more info at the end); you can enable these values by clicking resources gear icon -> show hidden resources at the bottom of resources tab.
¶ Defines:
f - faith at the moment of praising
wMLN - current worship (in millions)
ep - current epiphany
T - current Transcendance Tier
¶
¶
faith:
- resource generated over time
- Praise Bonus% (displayed on "Praise the Sun!" button) = + √(ep) × 44.7
- praise_Mult = ×(√(ep)×0.447 + 1)
- each 'Praise' will give f × praise_Mult worship [costs ALL faith]
¶
worship:
- gives boost to resources generation (assuming you have Solar Revolution)
- Solar Revolution bonus% (displayed next to worship) = + √(wMLN) × 44.7
- adore_Mult (displayed on "Adore the Stars" button) = ×(T+1)²
- each 'Adore' will give wMLN × adore_Mult epiphany [costs ALL worship]
¶
epiphany:
- gives boost to faith⇛ worship conversion (praise_Mult)
- each 'Transcend' will give 1 Transcendence Tier [costs 7.39T/ 313 epiphany]
¶
Transcendence:
- gives boost to worship⇛ epiphany conversion (adore_Mult)
¶
Note that all of the calculations in this section (except adore_Mult) are approximations and will not give exact results. The biggest errors occur for very low worship and epiphany values (<40'000w and <0.04ep will give >15% errors when calculating 'bonus%' values and up to 4% error in '_Mult' calculations) - however they definitely shouldn't be any worry at the moment of conversion as all the rest of calculations (including the most important conversion calculations) approximate with < 3% error margin, the same error values for ep and wMLN. All errors are slight overestimations from what I could gather. Also, I have been using these formulas with no issue whatsoever through Transcendance Tiers 4-6 and epiphany values 75-3800 and any errors have been negligable so far and are only getting smaller over time.