## No Variation Or Shadow Of Turning: Calculus In The Bible

Edit:  02/24/2011, to make a point about path integrals more plain.

Even though Calculus was not “discovered” until the late 17th century by Sir Isaac Newton and Gottfried von Leibniz, there is one verse in the Bible that makes a very excellent point in biblical and mathematical language that I would like to share for two reasons:   1.  It’s sufficiently nerdy to have escaped common attention.  2.  I have an odd interest in areas where seemingly different fields connect.  So, here goes.

James 1:17 says:  “Every good gift and every perfect gift is from above, and comes down from the Father of lights, with whom there is no variation or shadow of turning.”  There are several possibilities about what is meant by the enigmatic phrase “shadow of turning,” as some have suggested that this refers to the orbit of heavenly bodies [1], which I consider at least a possible, if not certain meaning.  Given that I do not believe the Bible only has one layer of meaning, though [2], I will discuss a mathematical meaning for this verse.

Let us begin with the assumption that as God is the ruler and creator of all things that this includes mathematics.  If we concede that among the good gifts that God gives and part of the “light” of illumination that He provides is an accurate understanding of mathematics and its implications, let us then examine the mathematics and implications of this particular verse.

First, to say that there is no variation with God is to say that the dGod/dt = 0.  That is, the derivative of God over time is constant.  God does not change change with time–he is the same yesterday, today, and forever (Hebrews 13:8).  As this very quote is stated in scripture, it is an accurate biblical statement expressed in the language of calculus.

Second, though, there is no “shadow of turning” with God.  If we take variation as the first derivative, it would make the “shadow” of turning the second derivative.  In other words, dGod^2/dt^2 = 0.  This is an important mathematical statement for a few reasons.  For one, the derivative of a function equals 0 at either a minimum, maximum, or inflection point, but additionally stating that the second derivative is 0 means that God is a straight line, completely level, with no change at any point in the existence of the universe.  This is a very profound statement–a nerdy one to be sure, but profound nonetheless.

Another option, of course, is described in the article cited below [1] and states that the “shadow of returning” refers to rotation, which would make the dtheta/dt = 0, and would make the first derivative of both the path and the standard integral equal zero.  At this point I am reminded of the difficulties I had understanding the subtleties of Green’s Theorem when I studied Calculus as an undergraduate engineering student, but this would similarly mean that God was without variation, regardless of how it is measured over time.  In short, God is level–however one defines it.

The fact that God is “level” has a lot of implications.  For one, it means that God is completely fair and just and consistent–something that may not be readily obvious in the fallen and corrupt world we live in but will be made very plain in His judgment.  Furthermore, his standard is a just and a fair one, not an arbitrary one as is the case with mankind.  God does not play favorites, but both merciful and fair.  That’s a mathematical truth we can all feel joyful about.

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### 56 Responses to No Variation Or Shadow Of Turning: Calculus In The Bible

1. tyler says:

hahahaha,
that is rather nerdy, my friend. i love it. though i am unconvinced shadow of turning is a derivative of no variation. especially since it refers to rotational motion, while variation is any kind of change. perhaps dG/dtheta would be a better description of the other derivative?

• Actually, that’s a good way of putting it. I had commented, briefly, that no “rotation” was also a meaning of it that I thought was quite profound. I guess it would all be determined by what was meant by “shadow of turning.” That would get really nerdy, and probably require some reading of Greek astronomical texts.

2. fresnojoe says:

lol ~ Amen~!

3. Rudy says:

funny stuff.. enjoyed the article and the comments.. thanks to all nerds in the world!!!

• I’m glad you enjoyed it; I like being a biblical math nerd on occasion.

4. Linda says:

I would like to go deeper into the rabbit hole — regarding “turning.” In the ancient text “Pistis Sophia,” Jesus said that at His ascension, he made some changes to the cosmos. Up to this point, as I understand, the planets and stellar bodies had turned to the left. We have historical records proving that magicians, astrologers, diviners, etc., all through history, have used the paths of these planetary bodies to “fortune-tell.”

It’s a complicated passage. If you enter phrases like “turn to the left” or turn to the right” in your search tool, you will find these long paragraphs in “Pistis Sophia.” Since I’ve never delved into horoscopes or charting the planets, I don’t understanding how the changing of the orbits — turning from the left side to the right — would affect this “fortune-telling.” Perhaps you, as a math person, could shed some light?

• Are you talking about gnostic mystical texts? You can research those all you like, but they demonstrate the interests of the heathen and not my own. I’m not particularly interested in astrological matters myself.

5. Scott says:

I agree completely with the sentiment and truth in what you wrote and I, too, revel in it. With no intent of criticism whatsoever, may I point out a subtlety? Math is not ordained by God as truth. It is simply the language we use to describe a situation or reality. Different people choose to describe the same situation differently, though coming to the same conclusion of truth. Some measure in centimeters, and some in inches. Some count in binary, some in hex… Math is not truth. It simply describes truth, which exists and continues to do so at God’s bidding. Math and science are our understanding of this truth, but are still incomplete and inaccurate. God is able to bend the physical (not that he would change the moral) truth in the universe to bring the miraculous to pass, rendering math and science useless in that moment. Sorry. Don’t mean to be verbose, just an observation.

• No offense taken. That is a worthwhile observation to make.

6. Joshua says:

Very interesting. I am not familiar enough with the Greek, but couldn’t the reference be to a turning in which there is no shadow? In other words, there is a turning, but there is no shadow – which would be akin to the angel from Genesis who has a flaming sword which turns every way. Perhaps like the sun, it turns but there is no shadow in the turning because it is purely light.

• That would be an interesting possibility as well. It does seem that in general translations recognize it as an absence of variation, but I do like that idea of your as a secondary interpretation of the scripture (we must be aware that scripture often speaks truths on multiple levels, so there is no harm in looking at the other ways in which a given phrase may apply rather than a very basic understanding of mathematical principles, as my blog entry was focused on).

• Charlene says:

The shadow reference given in God’s word gives us the understanding that God shows no favoritism. We all are made in the image of God & many believe after the fall of Adam’s disobedience that man’s image became corrupt with sin. This is not true coming down from the father of lights he cast no shadow upon mankind. It is God who forms each and everyone of us in our mother’s womb (Psalm 139:13,14; 119:73; 100:3; Mal.2:10). We were made in the Image of God who is Pure & Holy (Gen.1:26,27; Gen.9:6; 1 Cor. 11:7; James 3:9; Zech. 12:1; Job 33:4; Acts 17:25,29). It is man’s choice to disobey God and he will be held accountable for his disobedience at Judgment Day. Many false religions like ‘Calvinism’ says God arbitrary. Our God is a just and a fair one, not an arbitrary (Leviticus 19:15; Deuteronomy 10:17; 2 Chronicles 19:7; Proverbs 24:23; Acts 10:34; Romans 2:11; Galatians 2:6; Ephesians 6:9; Colossians 3:25; James 2:1; 1 Peter 1:17).

• Very well said.

7. I heard it said by evangelist Reinhard Bonnke that the phrase “shadow of turning” was used back in the day to refer to sundials. No shadow of turning means 12 noon. Hence, God is always at full strength; he never rests.

• That’s an interesting reply; I’d like to see where he got it from.

• H says:

There are no shadows in heaven. There is no sun to create shadows there as our Creator is the Father of lights. As our planet rotates shadows are formed, day to night, and very interestingly the shadows in the morning are long and shrink and turn forming opposite to the source of light (sun during the day, moon at night). After noon the shadows grow longer again. Who is our source of truth? For me, the Father of lights, his son Yeshua (Jesus) and the Comforter(Holy Spirit).When you walk in the light of the truth, being in God’s will and living His Way, there are no shadows. Shadows are formed only when there is an absence of light. Yeshua said I am The Way, The Truth and The Life. Life without shadows……awesome!!!!!

• That is true, there are no shadows, but that is because there is no variation of the kind that we know here.

8. Lex says:

This is awesomely interesting! I don’t really understand the whole derivative thing but I get the gist of what you are saying! This is good! Is there anyway you can break down the whole derivative thing down further for me? Like Calculus for Dummies??

• Calculus for dummies. Well, it’s been a while since I took Calculus myself, but a rough explanation of a derivative is that it is the slope of an equation. For example, the derivative of 2x+3 is 2, as that is the slope of the line. I’m glad you found the blog post interesting; it’s certainly something I have found intriguing to think about as well from time to time.

It is rare to find people tossing around fresh ideas like this! Loved reading this. I wonder at times about the verse in Malachi 4:1 where it says “the sun of righteousness shall arise with healing in his wings”. Someone else here mentioned the sun and even though it rotates is always at full strength and so I thought well, maybe the rays of the sun are those “wings” in symbiol that cast no shadow. Pursuing that thought even further, the light of the Lamb and His presence in the holy city eclipses the physical light of the sun in the New Jerusalem where there is no night and thus no shadows, and the tears of all of the people are wiped away (mercy/forgiveness/healing) by Christ.

• Thanks for your fond statements. I must say that I have not written a great deal about the matter of the “sun of righteousness,” but you do bring up a good point about connecting it with the end of Revelation.

• H says:

Revelation 22v5 And night shall be no more; they need no light of lamp or sun, for the Lord God will be their light, and they shall reign for ever and ever.
The New Jerusalem on the new earth.

Awesome interpretation! Yes I too love to explore the parallel connection between two completely different fields.

11. Rosemary says:

Thanks a lot for helping us understand this. I was meditating on that scripture, so I decided to browse what the meaning is, to let it sink into me more that’s how I came across your post. Am glad I did.

12. Jo says:

I, like Rosemary, was meditating on this verse and found your post as a result. I laughed with delight over your mathematical, true to Scripture, interpretation of this verse. This morning before I read this, I was thinking about how often I hear things mathematically. I pine over statements made that are not brought to a conclusion. Sometimes things are said that are meant to be profound, but I want to say, “therefore………… Because of this, then……………” It truly was fun, as well as enlightening to find your post. Thank you!!

• You’re very welcome. I do admit there are some intriguing thoughts one comes across when one thinks mathematically, and I’m glad you found it delightful and humorous :).

• Kenji Uhden says:

I came across this too trying to look deeper into the verse! I’ve always felt mathematics was a language of God.

• Excellent. That’s why I wrote it, being interested in mathematics and its relationship to God :).

13. Martin Pennington says:

I have coined the terms newtionen theology which I discribe as cause and effect and Quantum theology which I understand as dualistic neither partical nor wave but symptomatic of something else. My struggle then is to understand paradoxes like how can God (father) be fully love but also just and fair. To me then a shadow of turning means a variation in love dependent on the nature of our actions ( cause and effect) that variation being justice. But for me justice is not part of God but part of us ( more partical less wave ). Once again God is pure love no more nor less.
One ultimate consiquence of this relates to how He is viewed ether He is so good and pure he is beyond a relationship with, which is how many see Him. Or, dispite the paradox he never judges never condemes because His relationship is built not on cause and effect but on something so beyond understanding yet so intimate it is only hinted at by the models we have.
Or the Love as we know it. ☺

• The apparent paradox between the love and justice of God is one that many people struggle with in the contemporary world, as it is easy to be loving and not particularly discerning and pitilessly just but not particularly loving, but very difficult to be both.

14. Dave says:

This is wonderful! Thank you for the encouragement🤗

15. Kenji Uhden says:

Nice I love it.

16. Blessing says:

That was great, we often see mathematics to be so abstract, specially calculus but with this I think it is very real concrete because even in the bible mathematics is there .
Thanks for the incited though.

• I’m glad you appreciated the article 🙂 I enjoy looking at mathematics in a way that is less abstract than usual.

17. Josie says: