There are some set phrases in Japanese that involve adjectives becoming nominalized by simply being left as is. As quick examples, consider the following set phrases.
To know full well about the world.
Literally: To fully distinguish between sour and sweet.
Typically, however, ～さ and ～み are used to nominalize adjectives, with ～め and ～き being additional more complicated items to choose from. The resulting products of these endings are not completely interchangeable.
～さ nominalizes an adjective objectively. Nouns with ～さ can either be concrete or feel as if they are. Not only can you find it after 形容詞, but you can also find it after 形容動詞 of both native and Sino-Japanese origin as well as loans from other languages.
How long is it?
To enjoy happiness.
3. 無鉄砲さだけは親譲り。 (皮肉的)
Only recklessness is from (his) parents.
Rapidity of stability
Difficulty of taking medicine
I was moved by the flower's beauty.
To accomplish with strength.
9. 土地の値段は広さと｛利便性・便利さ △｝で変わります。
The price of land changes according to the size and convenience.
The blow was strong enough to knock down a tree.
The weakness of capital investment could became a big minus to competitiveness.
Wanting to eat his hometown's Sanuki udon, Yukito decided to go back home for the day.
Grammar Note: This shows that ～さ can be used with ～たい phrases.
It's the lull before the storm.
Form Note: 静けさ is from the Classical Japanese 静けし. Note, though, that 静かさ does exist because 静けし and 静かなり were different words then. 静かさ describes the objective quietness of something whereas 静けさ describes quietness in the sense of tranquility, emphasizing that quietness is a prerequisite.
Warning Note: 大げさ is not an example of this. The true spelling is 大袈裟, and this is not 当て字. Rather, 袈裟 in this phrase comes from 袈裟懸け, meaning "slashing someone diagonally from the shoulders" in this instance. This eventually led to its adjectival meaning of "grandiose".
To forgive out of consideration of (the person's) youth.
Phrase Note: ～に免じて = "in mercy to". It comes from a feeling of compassion. Other things may be more appropriate in a given context. The thing normally dismissed/forgiven is typically a crime or blunder of some sort done by someone.
In mercy to me, please release the prisoner.
～み nominalizes an adjective subjectively. So, ～み shows that there is some sort of condition or nature. It may also show the "location" of a certain condition. For example, 高み means "elevated place". The 当て字 味 is often used to write ～み.
Grammatically speaking, ～み is very limited as to what it may attach to. It must only attach to simple adjectives (単純形容詞) such as 苦い. Derived adjectives, compound adjectives, and adjectives with repeating parts like 美々しい, cannot be used with ～み. This is the complete opposite with ～さ.
Most of the adjective it can be used with refer to sight, hearing, hues, significance, etc. However, even this is not good enough. The chart below has almost all existing examples in Modern Japanese. To really know how み works, you have to investigate into each one. Some commonalities exist between similar words, but that's about it.
Some of these are so rare that they may not be recognized as existing words by natives. For instance, 軽み and 長み no longer used. Some may be viewed as coming from verbs (痛む → 痛み; 楽しむ → 楽しみ; 悲しむ → 悲しみ; 明るむ → 明るみ; 暗む → 暗み).
1. 白み may be read as 白身 to refer specifically to "egg white", and 白味 can be used to refer to "whiteness" or "egg white".
2. 黒み may also refer to "dark feeling" instead of just "dark hue".
3. 黄み spelled as 黄味 or 黄身 may mean "egg yolk" with the last option only meaning "egg yolk".
4. 浅み (shallow place), 低み (low ground), 軽み (light hue) read as either かるみ or かろみ, and しょっぱみ are high candidates as being "ungrammatical" to people due to their rarely used status. It is to note that かろみ is actually a complex word from 芭蕉 works referring to a serious and smooth figure for discovering beauty. It's also important to note that although many Japanese teachers will tell you that しょっぱみ doesn't exist, it's not difficult to find examples of it made by native speakers. Perhaps this is due to confusion from み’s multiple usages in the Japanese lexicon. On one hand, しょっぱみ refers to salty flavor, not saltiness, which then it would need to be replaced with しょっぱさ. However, spellings such as しょっぱ味, 苦味, 旨味, and 甘味 hone on this meaning.
5. 高み, 低い, 深み, and 浅み refer to places and not degree.
6. 臭み may be used figuratively.
7. うまみ has several meanings, which include "good taste", "the fifth category of test 'umami'", "skill", and "profit (商売)". It's interesting to note that umami has been introduced into English.
8. 暗み no longer exists from the adjective 暗い, though it is productive when derived from 暗む.
9. ありがたさ ＝ gratefulness; ありがたみ ＝ value; importance.
10. 重み may refer to a weight that feels heavy, heavy in the feeling sense, or heavy in the abstract sense. Thus, as you can imagine, 強み and 弱み are based on feeling rather than on concrete strength. This sense is also true for 厚み, 温かみ, 柔らかみ, and 温み.
11. You do not derive 温かみ 柔らかみ from 温かな or 柔らかな.
12. ありがたみ is an exception of み not being with compounds.
Something that's reddish
To go in too far.
It was brought to light.
A snake is squirming in the grove.
Word Note: 茂み is an example where the original adjective is no longer in existence.
With the passing of my mother, I experienced gratefulness for the first time.
It lacks freshness, but it is a plan that will bring over a lot of people.
Word Note: 新鮮み may be viewed as an exceptional case, but 味 in this instance can also be viewed as literally being Sino-Japanese, in which case this would not be a suitable example.
It's a plan that lacks freshness.
～め is yet another ending that may nominalize a subset of adjectives. It is even more restricted than み. It may be used with dimensional adjectives (次元形容詞) such as 長い, 短い, 太い, 近い, 遠い, 高い, 低い, 細い, 丸い, 厚い, 薄い, 深い, and 浅い.
There are also other examples such as 多め, 早め, and 古め (not so common).It can also be with some color: 黒め; 白め. You have to be careful, though, because 赤目 does literally mean "red eye(s)". In speaking of which, 黒目 do mean "iris" and 白目 "white of the eye". So, using ひらがな instead is wise to differentiate meanings. These words in which there could be conflicting meanings are best used in phrases. In fact, all of thee words are most frequently used in larger phrases.
The purpose of ～め is to show degree or tendency. And, it may also be seen after some verbs. Important examples include 控えめ and 落ち目.
To tear up a field deep.
Anime songs with a lot of English
Light on pigment
A rather thick cloth
Spelling Note: There is no true difference in spelling if you use め or 目 aside from the color examples. However, it is less common when it attaches to adjectives.