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Events happen within the continuum. Those events have physical manifestations that have beginnings that are discreet points in time.

Of course there are points within a continuum, but it is the nature (and the definition) of any continuum that adjacent points are not significantly different. Thus any chosen beginning becomes arbitrary.

Nevertheless, at one point, there's a white patch then there's a letter.

With photon generation, you chose an example where quantum scales may be significant for one photon of each dot of the letter (on a CRT, electron excites phosphur atom which emits a photon without apparent smooth transitions). However, for the entire letter that you see, there is a delay between each dot on the grid, which are not lit simultaneously. These photons leave the screen phosphors at different times, travel a distance from the phosphors to your eyes, through your cornea, aqueous humor, lens, vitreous humor, plasma membrane of a photosensitive retinal cell, and excite a molecule of rhodopsin (another quantum event). Then, the 11-cis-retinal moiety of rhodopsin changes shape to form 11-trans-retinal, a series of chemical reactions produces metarhodopsin from rhodopsin, metarhodopsin activates cyclic-GMPases which, through another series of chemical reactions that lead to ion transfer, changes the transmembrane potential of the cell. Then, when enough photons excite enough rhodopsin molecules, the membrane potential changes sufficiently to stimulate electrical signal propagation to an optic gangion cell, then through the optic nerve, optic chiasm, opic tract, optic radiations, to the visual cortex of the occipital lobe. These propagating signals can also be broken down into a series of chemical events. From there signals propagate to other areas of your brain that result eventually in perception of the letter on your computer screen. I say eventually, because a single photon, especially in a lit room, will not be sufficient for you to "see" even one dot of that letter, let alone the entire letter. It will take several retraces of your CRT to generate enough photons for you to perceive the letter.

Of course, I've left out many steps in this process. But where among this continuum would you place a nonarbitrary dividing line to call the "beginning" of that letter? All time points in the gradual transition from 'no letter' to 'letter' are essential, but no adjacent points are different enough to place a nonarbitrary dividing line. The letter does not just poof into existence.

Nature transitions everything too smoothly (above quantum scales) for specific dividing points to be nonarbitrary.

Easy, when I can measure it (egocentric grin).
I still can't figure out why you're picking at this point, why you think that defining and dividing sequences of events changes the status or state of the not-quite-14 day old embryo.

Even within the continuum, energy and matter undergo changes that are discrete. Choosing which change is significant as the end of one reaction and the beginning of another is not necessarily arbitrary -dictionary definitions notwithstanding - although, for us humans, it may seem to be since it's a matter of ability to measure and detect and report.

With better reflexes, technology, and knowledge, I might be able to detect the letter sooner than a presbyopic unenhanced middle aged lady. The fact that the good-reflex-me can detect the beginning of the appearance of the letter sooner than the middle-aged me does not change the fact that there was a first change on the screen.

For that matter, even if the observer has a cataract and sees yellow, does not change the actual light given off.

The fact that there are infinitisimal steps in fertilization does not change anything. The fact that scientists will disagree on when the cell may be called a zygote as opposed to a fertilized oocyte, does not change anything - there is a time when there is no human being in the fallopian tube or petri dish, and then a time when there is.

At that point, there is a new human being that has the right not to be killed intentionally by another human, unless the new human is a danger to the life of human being(s).

Carnley denies that the zygote "is a human life" because he wishes to justify killing zygotes and embryos.

My individual specialized cells do not have the right not to be killed, since they are a component of me, and, unless quite a number of them are killed, I, the human being will continue to live.

Oocytes and sperm cells do not have the right not to be killed, either. They are motile, specialized cells, but they never demonstrate "Growth with Reproduction, Inheritance, and Variability." Even the stauchest no-contraception advocate will not consider that a human being's life is taken with spermicides or condoms or if ovulation is blocked.

At your rate, we'd be defending life "before you were a twinkle in your father's eyes."