One of the strangest doctrines in all of Christianity is the doctrine of the Trinity. This doctrine holds that there are three divine persons — the Father, the Son, and the Holy Ghost — yet only one deity. Each of the three persons is fully God, and not just a part of God. A famous diagram known as the “Shield of the Trinity” compactly summarizes the idea:
The Trinity doesn’t make much sense, and many Christians recognize this. What most of us would call absurd they call a mystery, meaning something that is known to be true through revelation but cannot be demonstrated by mere human reason.
Some questions for the Christians out there:
1. Do you accept the doctrine of the Trinity?
2. Do you recognize the absurdity of it?
3. Do you deal with the absurdity by declaring it a “mystery”?
Your equation only becomes practical when the numbers are assigned to specific entities.
Say they denote sugar lumps, then the equation makes logical sense. What if they apply to mounds of sugar. Take three separate mounds of sugar, add them together and what is the result. You would have one mound of sugar. 1+1+1=1
I don’t take unity to be simple. I would say that a Bach sonata is a unity, but it is far from simple.
I am a physical individual and in this sense a unity. And I have previously referred to the body as nerve/sense system, rhythmic system and metabolic limb system. Three systems of equal importance of which I am composed. They are aspects of my unified body.
three
Then you should have said “Spirit is unity and multiplicity, and matter is unity and multiplicity.” The latter is obvious, and the former is what you need for the Trinity to exist as a spiritual entity.
Charlie,
Regarding “sugar mound math”, you’re overlooking some things. One is that the three mounds won’t necessarily be mashed into one. We could add them together in a way such that, say, five mounds are formed. 1+1+1=5. Will you suggest that we invent a new mathematics for every such scenario?
Or we can add them in a way that preserves their independent existence. That is, a way in which 1+1+1=3, and there are three mounds on each side of the equals sign.
Or take your sugar lumps and imagine throwing them in high arcs toward a target. When they hit the surface, they shatter into hundreds of pieces. Will you now invent a new mathematics in which 1+1+1=671?
Charlie,
Regarding Euclidean vs projective geometry, my position hasn’t changed. Neither is more dynamic than the other, and neither is more static than the other. You can imagine dynamic scenarios in both, and you can imagine static scenarios in both.
Charlie,
The sugar mound analogy has a theological problem as well. In that analogy, three lesser mounds are combined to form a larger mound. The three lesser mounds are each a part of the larger mound.
The analogy implies that the Father, Son and Holy Spirit are lesser beings that combine to form God. They’re each just a part of God
You are right. But on saying that we need to recognise the polarity. Unity is fundamentally spiritual, multiplicity is fundamentally material. Physicists have worked upon material and taken it apart down past the atomic level. But when this limit of the material is approached it is found that there are processes such as entanglement which leads back to unity, which is the spiritual pole.
We don’t need a new mathematics. We just need to understand what it is that we are equating. Three mounds on the left can produce 671 mounds on the right, but each side’s combined mass will be equal. We can play about with the material and separate it in any way we please but it still remains one substance.
In the video Euclid’s Elements: A Dynamic Geometry Perspective by Nick Jackiw, he says:
This allowed Euclid to ignore paradoxes of movement such as that of Zeno. He had a motive for trying to eliminate dynamism from his geometry.
It’s true, you can imagine dynamic scenarios in Euclidean geometry, but Euclid would have preferred it if you didn’t.
The sugar analogy is concerned with measuring physical substance. We cannot just take physical laws and think they apply to the spirit. The essence of sugar lies not in quantities but in qualities. Whether three mounds or one mound they still have the same essential attributes.
One physical symbol for Christ is the fish, the vesica pisces. This is an ancient symbol and it is formed during Euclid’s demonstration of the construction of an equilateral triangle (the symbol for the Trinity). A single straight line with two circles inscribed with their centres on its ends and circumferences running through the opposite end. The two further lines of the triangle derived from, begotten of the one single line.
Much can be discovered about this ancient fish symbol and Darwinians have as much justification for using it as anyone else. They take this basic symbol and make additions in order to symbolise Darwinian evolution. So this could be interpreted as earthly evolution originating from a primal spiritual condition. The physical derived from the spiritual.
Charlie,
since amended to
in order to correct your inadvertent exclusion of the Trinity from the spiritual realm.
How do you know the former? Which of Steiner’s orifices did it issue from, and why do you trust it?
Charlie,
Right. You can keep the old math in which 1+1+1=3 and the Trinity is incoherent.
There’s no reason to replace it.
Charlie,
1) You have no evidence for the spirit;
2) You have no evidence that if the spirit existed, it would operate under a different mathematics;
3) You have no evidence that if the spirit existed and operated under a different mathematics, that 1+1+1 would equal 1 in that scheme.
It’s pure wishful thinking.
My two statements are not mutually exclusive. There are two poles, the physical and the spiritual. I regard pure thinking as a spiritual activity. But our thinking can be driven from our will and our feelings in which case it becomes fragmented. I have already alluded to the Osiris myth which aligns well with this and with the thinking about the Trinity.
From the physical pole, each of us has a material body and so we regard ourselves as existing in the form of one individual organism. Each of us is a unity in our physical form.
I believe that spirit is unity through my thinking activity and my researches in striving to gain knowledge. Gaining knowledge is in itself a process of unification.
If for argument’s sake we assume that we are justified in regarding the human form as consisting of three aspects as I have said, the metabolic/limb system, the rhythmic system and the nerve/sense system, we can then look further into this. The limbs with their joints and mobility are the seat of mechanical activity and movement. The bones are long and radial with respect to the point which is the centre of the earth. Physical forces are dominant.
The head and central nervous system is predominantly the opposite of the limbs. The brain floats in cerebrospinal fluid shielding it from the full effects of the physical force of gravity. The only joints within the head that are freely mobile are the temporomandibular joints allowing us to move our jaws. The skull tends towards the spherical and is vaulted like the heavenly plane. The head is the seat of thinking which I have already said I believe to be a spiritual force.
Willing involves physical activity, thinking involves mental activity, and feeling is the connecting link between the two. The following shows where I see the connection between the trinity and the Trinity.
Thinking, spirit, Father.
Feeling, soul, Holy Spirit.
Willing, body, Son.
You did ask, so thank you for letting me expand on my thoughts 🙂
Physical objects can be dealt with in this way, but how do you apply mathematics to the spiritual which is taken to be pure being, pure love and wisdom?
Try this additional analogy:
Take a photograph and cut it into three pieces. You have three partial images that can be recombined to reform the whole. One image equals three partial images.
Now take a hologram and break it into three pieces. You now have three whole images in place of the one. One whole image equals three whole images.
Both of these give different results. Which one would you say was incoherent?
I regard thinking as a spiritual activity and so for me this is direct evidence.
It is a matter of what mathematics can be applied to. There are many areas in which a straight forward mathematical approach is inappropriate.
It is difficult, but I try to avoid wishful thinking precisely because it isn’t pure. Wishful thinking is thinking that is tainted with feeling. In that situation I would be letting my feelings control my thinking.
Charlie,
No, because each piece carries only the information from a distinct subset of vantage points. It isn’t the whole holographic image. So what you’re getting is just another variation of 1+1+1=3.
It also doesn’t work theologically as an analogy for the Trinity, because each of the three pieces is less than the single hologram with which you began the exercise. Orthodox trinitarian theology requires that the Father, Son and Holy Spirit each be no greater or less than the God within whom they all “reside”.
Charlie:
And:
So thinking is reliable because it is a spiritual activity, and spirit is unity because you think about it. Nicely circular.
Given CharlieM’s feelings about circles, he probably thinks that “circular reasoning” is a good thing.
But once freed from the tyranny of evidence, it’s possible to build fabulous superstructures of belief, in mind boggling detail.
Okay, let me ament the analogy. Replace the image with a vitally important written message that must be transmitted to three separate individuals.
The message is divided into three and given to each person. They can make no sense of it. But when each piece of the hologram is given all three individuals get the complete message.
The essential information which can be directly perceived and understood by each subject is transmitted in full; it is complete. The fact that the resolution of the writing is reduced is incidental and trivial.
I do not say that thinking is reliable. I believe that thinking is fallible.
My thinking activity is an undeniable fact that I am directly aware of. That is not to say that the contents of my thinking and the way I bring these thought contents into meaningful relationships need be reliable.
But any errors in my thinking can only be rectified by further thinking on my part. We unify reality through the process of thinking. And this is what I understand by the concept ‘spirit’. It is unified reality. But for me wholeness does not equal simplicity, far from it.
It’s quite good, but me absolute favourite is ‘triangular reasoning’. 🙂
The following passage from The Essential Goethe gives his views on infinity and being.
Being is not something that can be measured.
Just like circular reasoning but with an obtuse angle to it
Very funny. A cute reply 😉
CharlieM,
I’m here all week!
Goethe, as quoted by Charlie:
Where is the evidence that the choice of a unit of measurement creates “tiny, indefinable distortions” in the rest of the body? It’s a flat assertion. (Also note the weasel words “tiny” and “indefinable”. )
It appears that St. Johann, like St. Rudolf, is a fan of untethered thinking.
Charlie,
They can also be worsened through further thinking on your part. The problem is that when thinking is untethered to reality, it can go in either direction, correct or incorrect. Since there are many more ways to be incorrect than correct, untethered thinking will tend toward the incorrect.
Do you draw or paint? Have you ever done any life drawing? If you have you will understand what Goethe was getting at here.
You probably know that artists have always tried to standardise human proportions and to set canons. The image below gives an example of this. Now if you were to go to a museum and sketch a statue using the head as a unit of measurement you could probably produce a very accurate representation. Everything remains static, nothing changes.
Now try the same thing with a living model. They may look as if they are keeping perfectly still but there will be a constant imperceptible shifting of parts relative to each other. The person will be breathing and muscle tensions will be constantly changing. Shoulders will drop as fatigue sets in. You measure out one feature and from there move on to others only to find that when you return to the first feature its relative position has changed slightly which throws the subsequent work off.
Proportions can be laid out very accurately in still life but with a life model it is much more important to capture the various thrusts within the pose whilst keeping to the basic proportions as accurate as the situation allows.
You can measure with great accuracy the position of a supporting rod’s attachment on a mechanical structure. Try making the same accurate measurement of the location at which a muscle attaches to a bone.
A further comment to emphasise the point. A small flaw in the marble of a statue can be accurately measured relative to any other part of the statue. What would be the precise distance between the heart’s tricuspid valve and the base of the sternum?
Image from here
Of course you are correct that thinking can go either way. But when you say “unteathered to reality” what reality do you mean? Is it the reality of our everyday world of sense experience or the world of whirling, colourless, silent entities that supposedly exists behind the world of our senses?
I mean things as they actually are.
(Hence the ‘real’ in ‘reality’.)
Charlie, quoting Goethe:
It happens all the time. In medicine, for instance.
Says Goethe, without explaining how he knows this. And for fun, how does one determine this “highly spiritual” gauge?
Why not? Presumably he means that you’ll get an irrational number if you use the diameter as a gauge for the circumference. But so what? The measurement isn’t going to be accurate enough for it to make a difference And what’s so important about rational numbers?
How does the choice of the head as a measurement unit create “tiny, indefinable distortions” elsewhere in the body? Is this a “spiritual” process?
For what it’s worth, as a reading of Spinoza, that’s pretty good.
I’ve been reading Spinoza’s Ethics to pass the time while we’re socially distanced.
The main thing that I find really striking in this reading of Spinoza is how much he distrusts the imagination — it’s only in the intellect, and especially in mathematics, that we find completely reliable (because necessarily true) knowledge.
But Spinoza would of course be the first to deny that the Trinity makes any sense — it’s just another superstition of the rabble who lack proper mathematical training!
I’m sure you agree that in order to criticise somebody’s work and studies we need to have a good understanding of what it is they are trying to say. With Goethe this is made more difficult by the fact that we are reading an English translation of the original German and that his writing are from a couple of centuries ago.
Nevertheless, if you want to get a better idea of his way of thinking you can find the context of the quotes given above, here
Regarding trying to measure the circumference of a circle using the radius you would be correct in assuming that his point is that it cannot be expressed as a simple fraction.
My view on this is this disconnection between the two is due to the fact that they are an expression of polar opposites. Radii have their origin at the central point whereas the line at the circumference has is an expression of the line at infinity. Radii relate to the point, circumferences relate to the periphery. To inscribe a circle is to produce a trinity, creating form between two infinities.
Regarding the head as the unit of proportion. A holist might say that the head is actually an expression of the whole,
The mobile jaw is an expression of the limbs, both are moved through the action of the will.
The buccal cavity and tongue are an expression of the sexual organs. Through these we can create spiritually and physically respectively. The nose an expression of the lungs, and so on. The whole reflected in the parts.
Using the head as an aid to physically measure the body does the same as any such analysis, it kills the living form.
You mean by circular reasoning we determine that reality is what actually is.
From here
Goethe was a Spinozist for his fundamental creed was Spinoza’s ‘deus sive natura’. He once wrote a letter: “Spinoza does not prove the existence or being of God; the existence or being is God. And when others for this label him an Atheum, then I feel tempted to pronounce him Theissimum, or better still, Christianissimum.” And in another portion of this letter: “All effects in nature that we perceive depend upon one another…From the brick that falls from the roof, to the lightning brain-wave,…all these events are interdependent.” We can therefore call Goethe a determinist in the Spinozistic sense of the word.
Charlie,
Sorry, Charlie, but reading Torley-length quotes from Goethe (or Steiner) is just not worth the pain. Could you answer my questions in your own words instead? Or keep the quotes much shorter?
Charlie:
A circle is wholly defined with respect to the center. (Haven’t we had this discussion before?)
How do you know this? Is it via “clairvoyant investigation”?
And you know this how? And what does it even mean to “kill the living form”?
We can make these exchanges briefer if you just anticipate this question:
Charlie,
There’s no circularity, because our knowledge builds incrementally. Learning X does not depend on already knowing X; it depends on some other piece(s) of knowledge.
I do try to add my own comments along with any quote. I leave it up to you whether or not you deem it worthwhile to get some extra information. I don’t wish to compel you or anybody else to do anything.
Yes, coincidentally, we have just completed one full revolution of our journey round the sun since we were discussing this very topic here I will note that we view our distance to the sun in terms of space (radius), but we view our position in orbit in terms of time (circumference).
Hopefully, just like the solar system we’ve all moved on somewhat in the mean time, even if we are probably on divergent trajectories.
You are right, a circle is wholly defined with respect to the centre. Euclid defined it thus: “A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure equal one another. And the point is called the center of the circle.”
But there are two sides to a circle , the inside and the outside. By means of the central point the circle is defined, it can be measured. It is restricted within certain limits. In what way is it related to the outside? The outside has no limits, it can be expanded to infinity. It is beyond measurement. Radii are
segments, they have limits. Circumferences have no beginning or end. They are related to the periphery in the same way that radii are related to points.
One pole is limited which allows for definition and measurement. The opposite pole has no such restrictions and thus is beyond defining and measuring in this way. Regarding individual people, the body can be quantified by measure, number and weight, the spirit cannot. How do you weigh a thought?
The connection has been noted by others. lona Nemesnyik Rashkow posed the riddle, , “Why do men think so much and women talk so much,” and the answer given, “Because men have two heads and women have four lips.” Some Roman art works make the connection more explicit as in the image below.
Living beings are intrinically dynamic. Life drawing necessarily renders a static form which, if the artist were to represent with everything in the correct proportion and nothing more, the result would be a lifeless image. The great masters were able to use light and shadow and the thrust of lines drawn in a way that creates the impression of movement and in this way they bring the work to life.
I am not interested in the length of the exchanges as long as they give me something to think about.
Image source
In my opinion to say that reality is what actually is, is the same as saying what actually is is reality. It is circular.
I was trying to get you to explain what reality meant in your opinion, but you told me nothing new.
Perhaps, though it’s a matter of considerable debate as how well Goethe really understood Spinoza. From what I understand, Goethe has a poet’s faith in the power of imagination to construct metaphors that disclose rather than articulate certain truths. Nothing could be more antithetical to Spinoza!
Goethe believed his archetypes were directly perceived and not metaphors. He would study very thoroughly entities such plants or bone formations in as many states of their development as he possibly could.
His “exact sensorial imagination” was not to be taken as any type of inner fantasy. It was more akin to using the mind and mental pictures to survey the subject by means of time lapse photography before photography was invented. By this method he could “see” processes in nature that senses alone cannot give us.
He saw the unity of nature writing:
This view of the wholeness of nature is much more in agreement with the unitary nature of the universe according to Spinoza than it is to, say, the monads of Leibniz with its fragmentation of nature.
Here’s a question for Christians, anyone really.
Is this correct?
https://www.theguardian.com/us-news/2020/apr/10/wisconsin-voter-restrictions-democracy-coronavirus-primary
And this?
https://www.theguardian.com/us-news/2020/apr/08/trump-mail-in-voting-2020-election
It seems to be mostly correct. And so does the report that you linked in your next post.
Charlie,
The circularity is only apparent. I define reality as “things as they actually are.” I don’t define “things as they actually are” as “reality”. That was your addition.
Now, it’s true that those things will track each other, but that doesn’t mean that each is defined in terms of the other. And without the bidirectional definitions, there is no circularity.
To put it differently,
1) let A and B be our defined terms; and
2) let B be defined as equal to A; but not A as equal to B.
3) let c be some condition that qualifies an item to be added to A.
B will track A, but there is no loop. The causality runs one way:
condition c -> change to A -> change to B.
Charlie,
It also works the other way around, with the radius expressed in light-minutes and the arc length in meters.
The outside does have limits if there is a closed figure surrounding the circle.
Circumferences are unbounded but they are not infinite.
??
You can’t weigh thoughts, but you can’t weigh heartbeats either. Weighability is not a difference between “the spirit” and the body (even assuming that the spirit exists and is responsible for thought.
Charllie,
The Roman art is nice. Are there other cultures who used that motif? Also, what does it mean to say “is an expression of” in the above context? It sounds like it might be a Steinerism.