I will say you don't play op 10 no 1 with the fingers - that's everybody's mistake. You play it with the arms.
IMO, the essence of this quote -- you don't play piano with the fingers, but with the arms (and all the permutations capable therein) -- is the SINGLE MOST POTENT reason that separates pianists with amateur techniques from pianists with professional techniques.
There exist today whole schools of piano playing that emphasize enormous use of the arms and body to do what is the domain of the fingers alone. Largely these methods are misguided corrective efforts for injured pianists who sustained their problems through other misguided techniques e.g. arm weight/rotation, high finger, flat finger, etc., etc., etc.
To put it in simple perspective, its like someone who believes clarity of thought comes from hitting their head against a wall, but finds its painful, goes to a doctor, and the doctor prescribes alternative ways to bang one's head against the wall in order to reduce the damage.
With the piano, players expect to be able to use their relatively delicate fingers to assault the key board in all ways imaginable, and can't understand why they incur injury, inconsistency and undesirable musical results far from their hoped for goal.
Stop and think.
It only takes 50 gram or about the weight of 5 nickels to depress the key of grand piano. That is very, very little finger effort since the weight of one's finger is probably already in excess of that 50 gram threshold. Furthermore, since the inner workings of the piano mechanism behind each key come in contact with the hammer for only a few thousandths of a second at which time the hammer is catapulted into the string to produce the sound, why in the devil would one think it takes more than this tiny fraction of time and a very quick and precise effort to play a note?
I could go on here, but there's a very good article which speaks to this as well or better than I can, so for efforts sake, I'll simply refer to it here and pull in part of the essay.
First, just one other thought: If you ever DO "get it" and discover what true economy and the minimal controlled effort it takes to REALLY play as professionals do, you will quickly realize it and never want to go back to the "arm waving schools" and beating your head against a wall will never again be an option.
https://www3.sympatico.ca/norma.barr/library/piano/technique_piano_playing.html Three Essays on the Fundamentals of Piano-Playing
II. TECHNIQUE
Control of tone and dynamics is primarily dependent on physical training; control of timing is mental. Control of dynamics is control of hammer velocity; control of tone, as we have seen, means control of hammer acceleration.
If the movement of the fingertip begins above the key surface, it will be moving when it hits the key and will jar the hammer into vibrating. Thus, to avoid a percussive sound, it is essential that the fingertip be in contact with the key before the key is depressed. One depresses the key by pulling the fingertip down and towards oneself. A legato touch calls for a steady pressure on the key. A staccato touch calls for a sort of snap of the finger to send the hammer flying to its goal. The best way to check if one is achieving these effects is to listen to the sound produced when the pedal is down and the dampers off the keys. It is easier to distinguish the two cases by listening for the duration and strength of the after sound, rather than for the brief prompt sound. I also find it easier to hear the difference with loud notes rather than quiet ones.
Since one must always be prepared to use any or all fingers simultaneously, they must all be at the key surface at the same time. In their normal relaxed position, the palms of the hands tend to face one another; for all fingers to be in proper position at the same time, hands must be turned inward, so that the palm and back of the hand are horizontal. This position also facilitates the crossing-under of the thumb, as it keeps the outer part of the hand up and out of the way.
One wants to avoid depression of the keys by moving the whole hand downwards. Such a hand motion involves larger, slower-moving muscles and, hence, less sensitive control. It also compromises the independence of the fingers when balancing chords by imposing the same downward motion on all of them. The weak fingers of beginners, especially children, may not be strong enough to depress keys on their own, so that hand movement is necessary to produce an audible result. However, this should be regarded as only a temporary expedient to be abandoned as soon as fingers acquire sufficient strength.
All hand motions, except sideways to bring the fingers into a new position, are suspect. Rotation of the hand, sometimes recommended for a tremolo or Alberti bass, must be used very discreetly, if at all. Otherwise, when the thumb goes down, the little finger tends to fly up well above the key, and conversely. There is a similar danger when bouncing the hand from the wrist, as one might do in a rapid octave passage. Perhaps the standard admonition, "Keep your fingers close to the keys," should be replaced by, "Keep your fingers on the keys." Clementi, the founder of piano technique, apparently required his students to practise with a large English penny balanced on the back of the hand. Some people find this amusing, but the trick has a valid purpose. It forces the student to keep the back of the hand perfectly still and to do all the work with his fingers. While not appropriate for passages with leaps, the practice is still to be highly recommended. It immediately exposes weaknesses in the fingers. A Canadian two-dollar coin is an excellent substitute for the old English penny.
The requirement that the finger be in contact with the key before depressing it means that in moving the hand sideways to a new position, two distinct movements are required. First, hand and fingers are moved into position and in contact with the correct keys and only then, secondly, are the keys depressed. A student may feel that, particularly in long leaps, there is insufficient time for two distinct movements, but good pianists do it all the time. Any attempt to combine them into one will bring the whole weight of hand and arm crashing onto the keys, quite possibly the wrong ones, with a loss of control of tone and dynamics. Slow practice with the fastest possible movement to new positions has the advantage of embedding the correct movement in so-called "muscle memory" with a consequent improvement in both accuracy and memory.
Obviously, the sideways motion must be as fast and as free as possible. If the weight of hand and arm is allowed to rest on the keys, it has to be lifted off again before one can move sideways, thereby wasting precious time and impeding freedom of movement. Thus, hand and arm must be completely supported from the shoulders. The function of wrist, arm and shoulder is to move fingers into correct position as efficiently as possible and otherwise to stay out of the way. Complete relaxation of these muscles is essential as any tension has a blocking effect. One of my great-nephews, a trained athlete and kinesiology student, tells me that it is just as necessary to train the muscles that one does not use in an activity as to train those that do. Arms must swing freely from the shoulders. Computer users are frequently advised to keep forearms parallel to the floor to reduce the risk of repetitive strain injury. The same advice applies to pianists.
Shoulders serve as a basic reference point for the position of the hands on the keyboard. (Think of blind pianists.) It is therefore desirable that they remain in the same position whenever possible. And most of the time, except when both hands are needed at the same extreme end of the piano, it is possible. It follows then that the torso is normally still. Any unnecessary physical activity distracts both performer and listener from the music. Anyone familiar with the Alexander method knows the advantage of an upright posture with solid pelvic support. It gives observers the impression that the performer is in full control, and it has a similar psychological effect on the performer himself.
Subtle control of dynamics is essential both for the constant shading of melodic lines and for the balancing of chords. This, too, is best achieved with the fingers alone. if the fingers are forced to work regularly, they acquire the necessary muscular strength surprisingly quickly and, contrary to intuition, fingers alone can produce a bigger sound than any amount of arm action. This is explained by our theory of tone. If the keys are hit from above from any height, most of the energy goes into vibration of the hammer and a quickly vanishing prompt sound; there is little left for after sound. But almost all the energy generated by fast-moving fingers goes into a long-lasting after sound. (The pull of the finger on the key can be supplemented by a slight backward movement of the arm without any deleterious effects.)
It is true that the hands of many successful pianists fly up in the air, as pictures of Arthur Rubinstein frequently show. But this is just showmanship. Hands go up in the air when keys are released; they are back down on the keyboard before the next notes are played. Our claim that fingers alone produce the biggest sound is borne out by the example of Vladimir Horowitz. I quote the New York critic, Harold C. Schonberg, in his book The Great Pianists (Simon and Schuster, 1963, pp.410-11).
"...he was one of the quietest of pianists when seated before the instrument. His movements were precise, his body almost immobile." As a technician Horowitz was one of the most honest in the history of modern pianism. He achieved his dazzling effects by fingers alone, using the pedal sparingly." (My italics.) "And above all there were his stupendous fortissimos - that orchestral body of tone that only Horowitz could produce. In such a work as the Rachmaninoff Third Concerto he swamped the orchestra ..."
The loudness of a note is determined by the average downward velocity of the key. This must not be confused with the speed of motion of the fingertips. In normal playing with curved fingers, the finger bends as it depresses the key and the tip is pulled toward the performer. It feels as if the finger were pulling the key. The motion of the tip has both vertical and horizontal components; only the vertical component affects loudness. Thus, even if the fingertip always moves at the same speed - and it is desirable that it always move fairly quickly - loudness can be varied by changing the direction in which the fingertip moves. If the motion is almost vertical, a loud sound is produced; if almost horizontal, the vertical component is very slow and a soft sound results. Of course, there is a minimal vertical velocity below which the note fails to sound. It may be easier to control dynamics by direction of motion, particularly in pianissimo passages, than by speed of motion, but it is likely that most pianists unconsciously employ both.
With a level wrist, the motion of the fingertip can easily be varied over the full range from vertical to near horizontal. But a high wrist does not allow for vertical motion; in order to play loudly, it is necessary to poke down with the whole hand, with a consequent loss of control. Conversely, a very low wrist does not permit near horizontal motion, and control of pianissimo is limited to fingertip speed.
Occasionally. a teacher will recommend playing a passage with flat fingers. A flat finger must move almost vertically so that dynamic control through angle of motion is sacrificed. On the other hand, it also prevents a sharp initial impulse and enforces the uniform acceleration appropriate to warm tone and legato. Another useful device for dynamic control is to partially depress the key before playing the note. The distance travelled by key and hammer is reduced, producing a softer sound. It is most commonly used with repeated chords, or with trills, when the key is not permitted to come all the way back up when released. It also permits greater speed, since the fingers move shorter distances.
In sum, our ideal pianist (Horowitz?) sits almost immobile at the piano with a commanding vertical posture. His forearms are parallel to the floor, his wrists flat, his fingers curved. The backs of his hands are horizontal and unmoving except when they move sideways from one position on the keyboard to another. They are moved quickly into position by relaxed, freely moving arms, which are fully supported by the shoulders. Before any note is played, the finger is in position with the tip in contact with the key surface. After the finger is in position, the key is depressed solely by the pulling motion of the finger. Dynamics are controlled primarily by the angle at which the fingertip moves. Tone quality is controlled by the way fingertip and key are accelerated. Constant or increasing acceleration produces a legato touch with lots of after sound. An initial quick acceleration produces a staccato sound.