Mathematical science shows what is. It is the language of unseen relations between things. But to use and apply that language, we must be able fully to appreciate, to feel, to seize the unseen, the unconscious.

In enabling mechanism to combine together general symbols in successions of unlimited variety and extent, a uniting link is established between the operations of matter and the abstract mental processes of the most abstract branch of mathematical science.

Imagination is the Discovering Faculty, pre-eminently ... It is that which feels & discovers what is, the REAL which we see not, which exists not for our senses... Mathematical science shows what is. It is the language of unseen relations between things... Imagination too shows what is ... Hence she is or should be especially cultivated by the truly Scientific, those who wish to enter into the worlds around us!

It may be desirable to explain, that by the word operation, we mean any process which alters the mutual relation of two or more things, be this relation of what kind it may. This is the most general definition, and would include all subjects in the universe.

The further we analyse the manner in which such an engine performs its processes and attains its results, the more we perceive how distinctly it places in a true and just light the mutual relations and connexion of the various steps of mathematical analysis; how clearly it separates those things which are in reality distinct and independent, and unites those which are mutually dependent.

The Analytical Engine, on the contrary, can either add, subtract, multiply or divide with equal facility; and performs each of these four operations in a direct manner, without the aid of any of the other three.

We may say most aptly that the Analytical Engine weaves algebraical patterns just as the Jacquard loom weaves flowers and leaves.

Imagination is the Discovering Faculty, pre-eminently. It is that which penetrates into the unseen worlds around us, the worlds of Science.

I am never so happy as when I am really engaged in good earnest, & it makes me must wonderfully cheerful & merry at other times, which is curious & very satisfactory.

I am much pleased to find how very well I stand work & how my powers of attention & continued effort increase.

That brain of mine is something more than merely mortal, as time will show.

I think I am more determined than ever in my future plans, and I have quite made up my mind that nothing must be suffered to interfere with them. I intend to make such arrangements in town as will secure me a couple of hours daily (with very few exceptions) for my studies.

I believe myself to possess a most singular combination of qualities exactly fitted to make me pre-eminently a discoverer of the hidden realities of nature.

The Analytical Engine does not occupy common ground with mere 'calculating machines.' It holds a position wholly its own, and the considerations it suggests are more interesting in their nature.

I find that nothing but very close and intense application to subjects of a scientific nature now seems at all to keep my imagination from running wild, or to stop up the void which seems to be left in my mind from a want of excitement.

The science of operations, as derived from mathematics more especially, is a science of itself, and has its own abstract truth and value.

The ideas which led to the Analytical Engine occurred in a manner wholly independent of any that were connected with the Difference Engine. These ideas are indeed, in their own intrinsic nature, independent of the latter engine and might equally have occurred had it never existed nor even been thought of at all.

I have my hopes, & very distinct ones, too, of one day getting cerebral phenomena such that I can put them into mathematical equations: in short, a law or laws for the mutual actions of the molecules of the brain (equivalent to the law of gravitation for the planetary & sideral world).