Perhaps you just tried to save a document, only to be told you don’t have sufficient permissions to do so, or attempted to make another change to what’s on your Mac’s internal storage, with similar results. You then select the Macintosh HD disk in the Finder and Get Info. No wonder that didn’t work, as you only have read-only access to that disk. But if you unlock it and try to make any changes to permissions, you see

What’s going on?

Between macOS Mojave, with its single system volume, and Big Sur, the structure of the Mac system or boot volume has changed, with Catalina as an intermediate. Instead of Macintosh HD (or whatever you might have renamed it to) being one volume on your boot disk, it’s now two intertwined and joined together. What you see now as Macintosh HD isn’t even a regular APFS volume, but a read-only snapshot containing the current macOS. No wonder you can’t change it.

Root

Select the boot disk Macintosh HD in the Finder, and it appears to have four visible folders, Applications, Library, System and Users, just like it always did. Press Command-Shift-. to reveal hidden folders and all the usual suspects like bin, opt and usr are still where they should be. That’s the root of the combined System and Data volumes, and what’s shown there is a combination of folders on both volumes, with the top level or root on the Sealed System Volume (SSV).

The contents of those folders are also the result of both volumes being merged together using what Apple terms firmlinks:

• Applications contains apps installed in your own Applications folder on the Data volume, and those bundled in macOS on the SSV. You can see just the latter in the path System/Applications, where they appear to be duplicated, but aren’t really.
• Library comes only from the Data volume, and all its contents are on that volume. But inside it, in the path Library/Apple/System/Library are some components that should appear in the main System/Library.
• System comes only from the SSV, although it has some contents merged into it using firmlinks, such as those folders in Library.
• Users also comes only from the Data volume, and includes all Home folders for users.

So while the root of Macintosh HD might be in the SSV, much of its contents are on the Data volume, and can be written to, even though the root is a read-only snapshot, thanks to those firmlinks.

Data volume

There are two places that mounted volumes are listed in the Finder: the hidden top-level folder Volumes, where Macintosh HD is just a link back to the root complete with its merged volumes, and in System/Volumes, where what’s shown as Macintosh HD is in fact not the merged volumes, but only the Data volume. You can confirm that by looking at what’s in System/Volumes/Macintosh HD/System, where you only see the parts of the System folder that are stored on the Data volume, and not those stored on the SSV.

What is more confusing there is that System/Volumes/Macintosh HD/Applications is the same merged folder containing both user and bundled apps as in the top-level Applications folder. That’s an artefact resulting from the way that its firmlink works.

But if you open the Get Info dialog on System/Volumes/Macintosh HD, you’ll see the same as with the root Macintosh HD disk, information about the root and not the Data volume.

Mounted in System/Volumes are several other volumes like VM and Preboot, and (depending on whether this is an Intel or Apple silicon Mac) folders such as Recovery and xarts, that you really don’t want to mess with.

Permissions problems

Tackling problems that appear to be the result of incorrect permissions is best done at the lowest folder level. If you’re trying to save a document to the Documents folder inside your Home folder, select that and Get Info on it. Chances are that you are the owner and have both Read & Write permissions as you should. In that case, the problem most likely rests with privacy protection as in Privacy & Security settings. You then suffer Catch-22, as you can only effect changes to those by closing and opening the app, and as you can’t save your document before closing the app, you’re at risk of losing its contents. You may have better luck trying a different folder, creating a new one inside your Home folder, or using the Save As… command instead (which may be revealed by holding the Option key when opening the File menu).

Full layout

In case you’re wondering exactly which folders are merged into the hybrid Macintosh HD ‘volume’, those are shown below in increasing levels of detail, starting with the broad layout.

Then to a simplified version of the full layout.

Finally, in complete detail.

Happy navigating!

健身課表/課表中，除了動作選擇外，最重要的就是訓練強度和訓練量了。但訓練量有許多不同的定義，本文即是來解釋訓練量的定義方法及理由（原文請見 ig @vin_training）

簡介

訓練量，是大家耳熟能詳的名詞，是安排課表時重要的變因之一。

我自己最初接觸這個名詞時，學到的是「訓練量=次數x組數x重量」。但後來慢慢發現，不是所有人都這樣定義的。

譬如，許多健力、健美課表上的每日「volume」欄位就是指當天的「sets (組數）」。而台灣人應該也不陌生的 Juggernaut Training System 的 「訓練量專家」 Mike Isratel （水肥哥翻譯過他的「練胸完全指南」）也把訓練量定義為組數。

那訓練量到底該怎麼定義呢？本文整理了近幾年的研究並給出我個人的推論，但這並不是學界公認的定義，也不是每個健身者都認同的定義。事實上，有些專家會用更複雜的計算方式來定義訓練量（例如，考慮自覺強度或 1RM 百分比）。

因此本文主要目的是分享訓練量的「簡易定義方式」，以供大家參考，並不是說這就是唯一的正解。

For 肌肉量成長：訓練量=組數

傳統上，我們常用「次數x組數x重量」當作訓練量的定義，但就出現了一個問題：為什麼研究（1）會發現，當訓練量相同時，大重量訓練比小重量訓練能得到更多的肌肉量成長？之後，科學家發現，若把訓練量定義為「達到力竭的組數」的話，大重量訓練就跟小重量訓練有同樣的肌肥大效果（研究2，研究3）。

[實際應用]

在設計課表時，訓練量是我們常常要操作或控制的變因。許多人把訓練量視為「次數x組數x重量」，但或許把訓練量視為「足夠難的組數」會是更好的方法。

For 肌力：訓練量=組數

關於訓練量與肌力的研究相對不一致。有研究（4，5）發現訓練的組數越多，肌力成長就越高；但也有研究（6，7）得出高組數與低組數對肌力成長的效果沒有差別。

但不變的是，大重量對最大肌力的成長一定比低重量大。此外因重量跟次數是互相影響的，所以大重量必伴隨低次數。因此，以肌力為目標的話，將訓練量定義為「組數」即可。

[實際應用]

若目標是最大肌力，那一定要練大重量(>75% 1RM 夠的重量)，且時不時需要練>90% 1RM 的重量。但訓練量是不是重點呢？短期可能不是，因此比賽前減少訓練量是不會影響肌力成長的。但長期而言，因肌肉量愈高則肌力成長的潛力越大，所以高訓練量仍會比較好。

For 熱量消耗：訓練量=次數x組數x重量

當訓練量=「次數x組數x量」時，相同的訓練量會有類似的熱量消耗。

因為熱量消耗取決於做功，而做功等於「力x距離x總次數」。所以在距離相同的情況下（也就是你深蹲不會越蹲越高），熱量消耗就可以用「重量x總次數」來預測，而總次數就是次數x組數。

[實際應用]

如果你重訓的目標就是「熱量消耗」的話，那挑選較輕的重量確實能較有效累積一個訓練日的熱量消耗。但我仍會推薦重訓就以肌力、肌肉量、或肌耐力為目標，熱量方面靠飲食更有效。

另一個能觀察到的現象是，初學者通常深蹲或硬舉個 10 下後仍臉不紅氣不喘，但若是能蹲 200 公斤 10 下的人，蹲完肯定會攤死在地板上，因為熱量消耗實在太大了，所以休息時有氧系統需要火力全開提供能量。

結論

若你想尋求最簡單的方法來追蹤訓練量，那用「組數」算是不錯的選擇。但一組三下 vs 一組 15 下對身體的感覺確實不同，所以心中也要記得「組數」只是個訓練量的估算而已，最終還是要檢測自己的身體反應。