This is not about my pretending to be smart. There’s a great quote that I think is attributed to Mark Twain (perhaps a fitting way to start, I’m not even sure I have that right!) “A fool is a man who doesn’t know what you learned just five minutes ago”. I think we rarely approach the world with enough humility, these are a couple of things that make me feel particularly humble:
I thought I’d start with what’s going to seem entirely wrong, but I assure you is entirely correct. As my typing in this blog doesn’t include math formulas I’m going to use SUM() as being a summation (the addition of each element as defined by the sum from the first element to the last element. Here’s a really simple example:
SUM = 1 + 2 + 3 + 4 + 5 + 6 = (1 + 2) + 3 .. = (3 + 3) + 4… = (6 + 4) + 5 .. = (10 + 5) + 6 = 16
This is a fairly common calculation to make in math and in the sciences. In fact, it at least used to be taught in high schools under the title “SERIES” talking about infinite summations following a pattern. I’m keeping it simple here and not getting into series nor how sums are used.
There’s a special sum:
SUM = 1 + 3 + 5 + 7 … where the series continues, following the same pattern forever. Since there is no limit on this the SUM continues forever.
It turns out that this SUM = -1/6 as long as we go to infinity. Anything short of that and it is a very, very large number just shy of infinity. At the limit it becomes -1/6 and this bedazzles our brains.
Lest you think this is an idle curiosity a close friend who’s an astrophysicist tells me that this is measureable in some result in quantum mechanics.
Now I invariably get the proof wrong, so look at this page in Wikipedia that gets it right instead of me doing a bad job of it: 1 + 3 + 5 .. proof
In Physics there’s a fairly standard setup where you pass what’s known as coherent light such as light from a laser beam through first a single slit and then a pair of slits and record the result on a screen:
Note: I hope whatever Physics dept I cribbed this from is forgiving.
The light waves pass through the two slits and depending on where they arrive at the screen the interfere with each other creating light bands (constructive) or dark bands (destructive) interference. So far so good, we’re working with a light source we can pretend is putting out light waves and in one sense it is. Each photon sent out is a wave. Yet each photon is also a particle.
We repeat the experiment and send out very few photons using a source of light that is very sparing. The photons will almost never be going through the slits at the same time. Yet over time the same bands appear, why?
Unbelievably because each photon does go through both slits. The photon exists as a probability cloud of positions and that allows it to go through both. The probability cloud collapses when the position is measured by the screen in the form of, for example, a photographic negative. The amazing thing is that the uncertainty of the photon’s position is more than a theoretical thing, it truly is a physical thing.
We say, ok, we’ll try this again with a particle like an electron instead. That’s physical, it has mass where the photon has none. Same experiment, some adjustment of the slit because the “frequency” of the electron as determined by its mass is higher, but the results repeat. The electron too, even as single electrons go through both slits.
Confusing to say the least.
So why bring this stuff up, make us all feel dumb. Well, the math problem and proof go back more than a century. Interference patterns in physics go back a very long way, although I’m not quite sure when the started proving particle duality but I suspect long before I ever took university physics in the 70s.
We still don’t understand the world and the universe at the level of space that well. The universe is expanding. Why? We think there’s dark matter and energy because measurements are off, what is it that is making the measurements off and how can we measure it? We’re realizing that effects we thought only happened at the atomic and molecular level affect biology.
We have only the crudest understanding of intelligence, learning, memory and how those really work in the brain. I think when Sheldon Cooper makes fun of Biology in Big Bang Theory it’s because it’s sort of dark, scary and squishy (at least in my opinion).
Then I read something about a political ignoramus who says my sex is in my DNA. He or she takes this singular and not entirely definitive piece of information as if it were gospel and states with complete and utter certainty that it the answer.
Even as a non-biologist I dimly understand the difference between someone’s genotype, the coding contained in a person’s genes and the person’s phenotype, the actual expression of that coding into an actual living person. That expression doesn’t just happen once in the womb either, it continues throughout a person’s life as different cells react to the environment or signals like hormones being sent by the body or even by dysfunction.
“It’s in the genes” but if you were to make sure that a male embryo had no testosterone at 8 weeks of gestation you’d get some pretty odd results since that’s when differentiation of male and female sex organs goes on from the prototypical Mullerian ducts. Male babies who lack effective response to androgens end up looking just like any girl at birth and this is generally not detected until they don’t achieve menarche. (CAIS incidence est 1 – 20,000). Intersex conditions of all kinds including some that have no visual marker are around 1% of the population.
Biology is a very complex science but the workings of the brain make it look simple by comparison to me (no, I’m not saying bio is simple!). The first study to show that transgender brains had similarity to their cisgender targets was a paper which showed that MtF transsexuals had a similar neuron count in the BSTc portion of the brain as compared to women and FtM transsexuals had a similar neuron count when compared to cis men. They found that gender identity mattered, but sexual orientation and hormone status did not. Unfortunately the number of TS folks examined was relatively small because all of these were post mortem examinations.
Further studies have been performed that have confirmed the findings for the BSTc area in other sexually dimorphic areas of the brain. The abstract for a survey paper has a nice summary.
I hope something either piqued your interest, extended your world or opened your eyes. If not, it’s my failure for not being a better teacher.