Every mind which passes from doubt to belief must have ideas which follow after one another in time. Every mind which reasons must have ideas which not only follow after others but are caused by them. Every mind which is capable of logical criticism of its inferences, must be aware of this determination of its ideas by previous ideas. But is it pre-supposed in the conception of a logical mind, that the temporal succession in its ideas is continuous, and not by discrete steps? A continuum such as we suppose time and space to be, is defined as something any part of which itself has parts of the same kind. So that the point of time or the point of space is nothing but the ideal limit towards which we approach, but which we can never reach in dividing time or space; and consequently nothing is true of a point which is not true of a space or a time.
… ideas which succeed one another during an interval of time, become present to the mind through the successive presence of the ideas which occupy the parts of that time. So that the ideas which are present in each of these parts are more immediately present, or rather less mediately present than those of the whole time. And this division may be carried to any extent. But you never reach an idea which is quite immediately present to the mind, and is not made present by the ideas which occupy the parts of the time that it occupies. Accordingly, it takes time for ideas to be present to the mind. They are present during a time. And they are present by means of the presence of the ideas which are in the parts of that time. Nothing is therefore present to the mind in an instant, but only during a time. The events of a day are less mediately present to the mind than the events of a year; the events of a second less mediately present than the events of a day.
… Let us now see what is necessary in order that ideas should determine one another, and that the mind should be aware that they determine one another. In order that there should be any likeness among ideas, it is necessary, that during an interval of time there should be some constant element in thought or feeling. If I imagine something red, it requires a certain time for me to do so. And if the other elements of the image vary during that time, in one part it must be invariable, it must be constantly red. And therefore it is proper to say that the idea of red is present to the mind at every instant. For we are not now saying that an idea is present to the mind in an instant in the objectionable sense which has been referred to above, according to which an instant would differ from an interval of time; but we are only saying that the idea is present at an instant, in the sense that it is present in every part of a certain interval of time; however short that part may be. The first thing that is requisite to a logical mind, is that there should be elements of thought which are present at instants in this sense. The second thing that is requisite is, that what is present one instant should have an effect upon what is present during the lapse of time which follows that instant. This effect can only be a reproduction of a part of what was present at the instant; because what is present at the instant, is present during an interval of time during the whole of which the effect will be present. And therefore since all that is present during this interval is present at each instant, it follows that the effect of what is present at each instant is present at that instant. So that this effect is a part of the idea which produces it. In other words, it is merely a reproduction of a part of that idea. This effect is memory, in its most elementary form. But something more than this is required in order that the conclusion shall be produced from a premise; namely, an effect produced by the succession of one idea upon another.— Peirce, W3:68-71 (March 8, 1873)
Hsueh Tou directly says, “If you want to see the old yellow-face right now, every atom of dust in every land lies halfway there.” Usually we say that each atom is a Buddha-land, each leaf is a Shakyamuni. Even when all the atomic particles in the universe can be seen in one atom, you’re still only halfway there; there is still another half of the way yonder. But tell me, where is he? Old Shakyamuni didn’t even know himself; how would you have me explain?— Blue Cliff Record, Case 94 (Cleary and Cleary)