What would distance measurements in the Holy of Holies have been

The Gemara (Yoma 21a) says:

But didn’t Rabbi Levi say that this matter is a tradition that we received from our ancestors: The place of the Ark of the Covenant is not included in the measurement of the Holy of Holies. Based on that measurement, the Ark should not have fit inside the hall. The Holy of Holies measured twenty cubits by twenty cubits (see I Kings 6), and a baraita states that there were ten cubits of space on either side of the Ark. Therefore, it was only through a miracle that the Ark fit in the Holy of Holies.

From Shemos 37:1 we also know that the Ark was 2.5 amos in length. So we see that there was a miracle : 10 to one side of the Ark plus 10 on another plus 2.5 amos of the length of the Ark itself would be greater than the 20 amos of the Holy of Holies.

But what would happen if theoretically (since no one would actually be allowed to do this in practice) one would hold a tape measure from one side of the Holy of Holies to the other and note the markings on the tape where the Ark started (A1), the Ark ended (A2) and where the tape reached the other side of Holy of Holies (E). It seems like to be consistent with the facts from sources above, these markings would be:

• A1 = 10 (distance to one side)
• A2 = 12.5 (since A2-A1=2.5 is the length of the Ark)
• E = 22.5 (since E-A2 = 10, distance to the other side)

But then E (which would represent the length measurement of Holy of Holies) would be inconsistent with 20 as mentioned in I Kings 6:20. Since A1,A2,E would have to take on some values when measured, what would those values be?

• Maybe it's just not possible to measure. Like a velocity measurement from the point of view of a photon. Commented Sep 11, 2023 at 19:35
• In case of a photon there are several physical limitations that prevent carrying out a distance or velocity measurement (e.g. the mass [of a measuring device] can't be accelerated to speed of light, etc.). But what are the physical limitations to the measurement in the Holy of Holies? (We know the Kohen was able to do what seemed like physical acts inside - walking, sprinkling, and so on) Commented Sep 11, 2023 at 20:48
• FWIW, my guess is that the markings would be 10, 10 and 20. The Ark inside the Holy of Holies has no dimensions. The 2.5 amot was what used in it's construction, and presumably is also what you would get if you removed the Ark and measured it outside. But inside, it takes up no space. Commented Sep 12, 2023 at 7:05
• @user9806 that's not why you can't make a velocity measurement from the point of view of a photon. Similar to saying you can't measure the volume of a black hole Commented Sep 12, 2023 at 12:13
• Sure we could also say (for example) that a reference frame co-moving with light doesn’t even exist (to take measurements in) since it’d violate the second postulate of s.r. Commented Sep 13, 2023 at 5:52

Support for Heshy's point is found in the שער האמונה ויסוד החסידות, פתח השער לבית יעקב ה׳:

באמת מצינו במס' מגילה (דף י:) דבר זה מסורת בידינו מאבותינו מקום ארון אינו מן המדה.

In truth we find in Megillah (10b) the tradition received from our ancestors that the space of the Aron [in the Holy of Holies] wasn't measurable.

This is because the logic of measurement is a creation of Hashem, that is sustain in the human brain by His decree. Reality doesn't have to conform to it, and our understanding of it can change.

Indeed he explains this is exactly what the experience of the Kohen Gadol is; he goes into the Holy of Holies and witnesses the miracle but it does not appear miraculous to him, it simply makes perfect sense because while there Hashem alters the way he understands and perceives reality through his reason:L

שם האיר הש"י למעלה מן הסדר שהטביע בעולם, ולמעלה מן הסדר שסדר דעת האדם משכלו וידיעתו, וכל הנכנס למקום המקדש בקדושה ובטהרה היה רואה זאת גם בעיני בשר, והבין זאת בדעתו ושכלו

Hashem, blessed be He lit [the Beit Hamikdash] with a light that is above the natural order of the world, and above the ability of the normal order of reason in the mind of man. All who entered the Beit Hamikdash in a holiness and purity state would see this even through human eyes. He would understand with his mind.

• Fair enough, but the question here is not about a change in logic or a change in someone's perception while inside the Holy of Holies. It's a question about metzius/reality : Where would the markings on the measuring tape be, when it is brought out of the Holy of Holies into the (regular physical) world? Also, what does it practically mean to say that the space "wasn't measurable" ... Is it that the measuring act was not possible to do? (e.g. one wouldn't be able to carry it out, or maybe the markings would be erased from the tape?) Commented Sep 11, 2023 at 20:43
• @user9806 I'm not sure why you don't see this answer as answering all those questions. Please think about it more, check out the source in full, and I'll think if I can explain it better Commented Sep 11, 2023 at 20:49
• It's not clear how this answer addresses the simple question of "Where would the measuring tape have markings". The source you quoted discusses how human perception, logic, even the sense of what's possible and impossible can be changed by G-d. That still does not answer what the actual observed values from the measurement would be. A possible answer might claim that the measurement could not physically be performed. Or maybe that in the mind of anyone looking at the observed values there would be no contradiction (e.g. their logic and/or arithmetic would be altered). We'd then go from there. Commented Sep 11, 2023 at 22:11
• @user9806 it is saying that reality/metziut is different there, and our intellect in its current state cannot comprehend that different reality, so asking questions from the POV of our reality and our understanding of reality doesn't make sense. That's what he means by "not measurable". Commented Sep 11, 2023 at 22:47
• Right, but the original question was about a way to interface our reality with the reality there : by taking a measuring tape from our reality, performing a measurement with it in the reality of Holy of Holies, and then bringing the tape out back into our reality and examining the three measurement values in it. And so the question was simply asking what those three values would be. Supposing they are 10,12.5 and 22.5 respectively, then (now using the logic of our reality) we can say that means the total length is 22.5 amos and not 20. Commented Sep 12, 2023 at 0:49