There are many essential equations that describe the physical reality of the universe. Einstein’s E = mc2 is probably one of the most famous, and also the simplest. In the 1920s, physicist Erwin Schrödinger developed an equation that is of prime importance in quantum physics and chemistry. I first learned about (and worked with) this equation in an advanced physical chemistry course in college. The equation is critical in understanding the behavior of electrons, molecules and the wave functions of physics. Here it is:
It isn’t a simple equation at all – all of the terms have complicated meanings – but here I will only discuss one part of it.
Recently I saw an amusing post on Twitter by an atheist that was also in the form of an equation. It was this:
This was a somewhat clever attempt by the poster to say something about God. The square root of -1 (and indeed of all negative numbers) is called an imaginary number. So the atheist poster was trying to make the point that God is imaginary.
The reason such numbers are called imaginary is because the square root of a negative number doesn’t make sense. Such a thing violates basic rules of mathematics (actually the laws of arithmetic, see Sheila’s comment below) which say that the squares of all numbers, both positive and negative, are positive. Therefore, a negative number cannot have a square root.
But, unknowingly, the poster of this little doodle has made a profound theological point in direct contrast to the one he thought he was making. As it turns out, the square root of -1, while imaginary, is of critical importance in math and science. It is used often enough to have been given its own symbol: i. Now take another look at the Schrödinger equation above. Do you see the very first term? Yes, it’s an i.
So if God = i, then God is a crucial component in the basic laws of nature.
While this might seem a silly exercise in chastisement of an atheist with just enough scientific knowledge to get himself in trouble, there is also an important point here. And that has to do with what we mean by imaginary. God does exist in our imagination, and perhaps we cannot ever actually get a picture of the reality of God. Much like imaginary numbers. But this says nothing about the existence of God as a real and ultimate force in nature. The unintended metaphor of God being like the square root of -1 is actually quite powerful. Being imaginary does not equate to being false or nonexistent. Neither in modern science nor in theology (nor in many other areas). We already know that the basic principles of modern physics, from relativity to quantum mechanics, describe a world of reality that seems irrational to us. And here, again, we can use a metaphor from mathematics. There are also irrational numbers, the best known being pi, whose values can never be precisely known but only approximated.
So, if imaginary and irrational are critical adjectives needed to give an accurate scientific description of natural reality, how can the labeling of anything as imaginary or irrational (such as God) be an indication of non-existence? On the contrary, it would be quite strange if the creator and sustainer of all that exists were some analog of a 19th century clockwork maker or engineer.
I would like to express my thanks to the atheist who came up with this brilliant meme, and I can only pray that he (and others) will see, as I do, the miraculous hand of God in his unintended profession of faith.
(I am hoping that one of my most faithful readers, Sheila Deeth, a mathematician, will see this post and comment, especially if revisions are called for).
I love it!
I guess I’d say the square root of minus one violates the laws of arithmetic but is crucial to mathematics. And while arithmetic is great for balancing check books, we need math to balance science… and God to balance life perhaps?
Meanwhile irrational numbers can only be approximated in our numerical (arithmetical) systems, with the true value being so much more interesting and powerful than the approximation–pi is neither 3 (as it appears to be in Kings in the Bible), nor 22/7 (nor 3.142), but has to be known by what it reveals… just as God is known, not by calculation or measurement.
So, like I said, I love your post!
Good way of looking at it:). Maths fascinates me, but unfortunately I’m useless at it…but I do understand your comment about pi. I wonder if God deliberately made things so that it would appear (as far as I know) that some things cannot be measurable in absolute terms. Hence presumably forays into the quantum world etc etc.
Thanks, Sheila. You not only gave an important correction, but beautifully extended the interpretation and analogies of math to theology. I love the comment, and I think it should be seen as a collaborative addition to the post.
Thanks for this Sy. Profound truth is seldom simple or easy to hang onto! A reason why poetry and art, as well as mathematics and revelation, are so often the ways we can get a glimpse of it.
Thanks, Mark. Very true.
Reblogged this on Richard's Watch and commented:
Sy Garte’s post and Sheila Deeth’s comment surpass the concept of the conjunction of science and scripture to focus upon the metaphorical mirroring of maths and our Maker. Relish the truism behind an atheist’s jest.
Excellent post! I am absolutely lousy at maths so can’t comment on equations or anything. But because I do like to stretch my imagination and try and think around things, I thought to myself, well why can’t one have a negative square root? Well, perhaps there is a good mathematical reason, I don’t know.
What I do know is that it seems that a lot of people tend to say…oh, this, that and the other is impossible…and time and time again they are proven wrong. I would have thought atheists, especially scientists and mathematicians would be very well aware of that. Our knowledge of the world goes on apace, but I am pretty sure the surface has only just been scratched. In fact, it wouldn’t surprise me that if God’s existence could be proved mathematically or scientifically, it would perhaps be only God Himself who would know the equation! He probably laughs at people’s puny attempts to disprove Him!
Richard, thanks for you comment.
Yellowyarrow, welcome to the Book of Works. Thanks for the comment, and I think you are right. We like to think we know so much more about everything than our grandparents and great grandparents, but we dont stop to think about how much more people will know a hundred years or a thousand years from now.
🙂 And actually even people who lived housands of years ago knew things or how to do things that we have difficulty working out how they knew or did them!
Hi Sy, you may be interested to know that last October the Lord arranged for me to be in in touch with a lady who started receiving a series of prophetical ‘circuit’ messages. The first referred to maths and opens: “2018, I will impart to My Prophets the ability to see clearly ‘My Numbers’, such as dates, times and even denominations of money as I loose significant detail…”
Wow. Interesting. Thanks, Richard.
Hello again Sy. A couple of comments you may wish to read: 1 – Dave Hood in UK on my re-blog above; 2 – Phil View in NZ in the next post on recurrence of number 7 in dates in modern history of Jerusalem > https://richards-watch.org/2018/01/16/jerusalem-is-central-to-gods-prophetical-timeline/
I suppose it’s worth mentioning that the time-dependent equation itself is not precisely derivable. So how do we propose to derive the precise nature of Ψ?
Damned if I know. Its a great question, one that I believe I asked asked my phys chem professor, who basically answered some version of what Feynman was reported to say: “Shut up and calculate”. Anyway, welcome to the Book of Works, and I look forward to more questions (and maybe some answers sometimes) from you.
(As a side note, early in my online presence I used (at the suggestion of a friend, who is now my wife) the symbol Ψ (pronounced like my name, Sy) as my avatar. I will admit I often feel much like a non precisely derived wave function.)
My apologies if I appeared naive to the significance of the question. I assumed that you knew who was leaving the query (which may or may not be the case). But the question is sincere, and I appreciate the thoughtful response. I’m also writing this after reading “Elegance” and “STOP Signs”, both of which I think relate to this post (good articles, too).
Living in northern Thailand for several years, I was initially overwhelmed by the relative chaos there. I initially associated the condition with poverty and unhappiness. Regardless, and rather to my surprise, most of those around me were fairly satisfied in their lives, and remarkably happy. Likewise, burned forests aren’t especially appealing to my sense of decorum. But as it turns out, they’re a natural requirement for a healthy ecosystem. The idea here is, of course, that people can confuse an arbitrary human aesthetic with reality.
I know enough mathematics not to argue that what’s known of the discipline can explain everything. In fact, it may not actually be able to **explain** anything. Physicists understand that science and mathematics are two entirely different disciplines. Mathematics merely provides a convenient, if not fairly effective tool for descriptions. Even Feynman once conjectured that, “Physics, ultimately, will not require a mathematical statement.”
So it’s entirely possible that science is limited by a human attraction to the elegant… and such is mathematics. We’re enthralled that with a mere handful of axioms we can create amazing pictures of what we see around ourselves, and sometimes even puzzle out how things fit together. But then, looking more closely, we start to see the brush-strokes and the lines left by the hairs on the brush itself. We find that the tool has a limit, and that in the end it’s only provided a representation of the real thing.
I don’t know how one can derive the precise nature of what “is” either. But it doesn’t keep me from looking. However, I try to be careful not to confuse a lack of understanding or bewilderment with the justification of an aesthetic. I simply stare in perhaps ignorantly-blissful awe at the canvas spread before me… a perspective reflected in my own nom de guerre from those earlier times.
My sincere best wishes to you.
This has been a very busy week for me, and I was unable to find the time to look at your blog. Having now done so, I have a suspicion that I know who you might be. I must have had some unconscious inkling, which prompted me to write in my first reply to you that second paragraph about my avatar at an “earlier online presence” which if my guess is correct, you are well aware of. If you are who I think you are, then you must have used those powers of a Latvian witch to find me. I am glad you did, and I hope to see more of you here. Its been too long.
Yes indeed, and thank you very much for the kind invitation.
Hi great reading yoour post
The twitter post created by that athiest reminds me of something I hear people saying a lot, “There is no truth!” Well, if that statement is true, than it must be false, because it’s stating a truth. I have found some much truth in the quote, “there is no truth!” which is incredibly amusing to me. The same holds true for the equation the athiest created, which he happened to create out of his own imagination and therfore, by his own calculations, he comes to the truth that his own imaginary equation is false, because anything that is imagined is false.