When a Paradox is not a Disproof

The GPS is an amazing thing.

The chips in it work because of the physics of semiconductors, and the fact that the energy the electrons can absorb or emit come in fixed quantities. All of which is literally applied Quantum Mechanics.

The calculations those chips perform involve calculating the distance to multiple satellites by comparing the timestamp the satellites sent against the time they arrived. And then adjusting for General Relativistic effects caused by the satellite being in motion relative to the earth and the effects of the satellite being further from the earth’s gravity well. Then use the speed of light to convert travel time to a distance.

Using Quantum Mechanics to solve a General Relativity problem.

Here is why that is strange:

Quantum Mechanics (QM) which was born in the head of Max Planck and developed by numerous other people. Including Albert Einstein. It works well for the very small, atoms, molecules, subatomic particles, and the like. Relativity (which has two parts: Special and General Relativity) was pretty much entirely Einstein’s. It deals with the very large — planets, stars, black holes, where gravity dominates. (In between, Newton’s old system is a good enough approximation and people don’t bother with such things.)

But these theories are based on contradictory assumptions. For example, Relativity is  “Background Independent.” This means it isn’t about things that happen within space and time, but the nature of space and time is itself part of the theory. This is not true of Quantum Mechanics, which is about how particles and waves (more accurately: particles which are waves) move about and evolve in a background of space and time. Figuring out Quantum Gravity — a theory of gravity that fits both QM and Relativity, is a challenge. Filling this challenge are things like the various attempts to find String and Membrane Theories, Loop Quantum Gravity, and other proposals.

Because Quantum Mechanics and Relativity each work so well so often in ways they was not originally designed for, that the typical physicist is sure some resolution of the two that will preserve nearly all of both theories is out there, waiting discovery. After all, our GPS devices do work. So, even though the two theories are built on contradictory assumptions, scientists place trust (bitachon) in them. They have faith (emunah) that each will have to be tweaked only minorly to get them to fit, not a major overhaul.

For similar reasons, science vs Bereishis questions don’t really bother me. Neither is really about what happened in the past. The central theme of religion is whether the values, ritual, and system of thought work. The issues of genesis, the flood, or the tower of Babel are tangential, and out the outskirts of the Torah as a “theory” of meaning and purpose in life.

Scientific theories make claims about the past to explain what we observe astronomically and archeologically. The Torah tells us about our past to help us work toward our future. These areas of conflict really are side-topics in each discipline. Like bringing in Quantum Machanics to explain the Relativistic effects of Black Holes.

It might even be that the reason our generation finds these topics so pressing is a flaw in today’s zeitgeist. Science and technology have brought us so much since the Industrial Revolution that we perhaps forget that it’s not the only venue. As Rabbi Soloveitchik would put it, Cognitive Man is so successful “fill[ing] the earth and subdu[ing] it”, as per Hashem’s blessing of Adam in Bereishis 1, that we forget the Lonely Man of Faith. We feel a pressure to get our religion to play ball on science’s court, when in reality we are looking at the fringes of what religion is for.

Truth must be consistent, but these problems of origins are not pressing ones.

Each “theory” works so well so consistently in their own domains, I presume that some resolution will someday be found — much like a quantum mechanical understanding of gravity, an understanding of the small-scale workings of a phenomenon only significant in the large scale. One cannot ignore science in the pursuit of the Divine, but neither can one ignore the Torah; nothing is gained by wallpapering over one source of truth in favor of the other.

And in the meantime, I can use Torah and science simultaneously to find my way in the world. No less so than my GPS.

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  1. Very well put. I have also written much about it. Theology has to fit with reality. It has to adapt to new reality as we discover and understand it. Ki Hi Chochmaschem Ubinaschem ….

  2. micha says:


    You motivated me to expand my post. I do not agree that “Theology has to fit with reality. It has to adapt to new reality as we discover and understand it.” In fact, I am saying that while there is only one truth, don’t rush to adapt the theology rather than the science. Often it’s better to wait than to do any adapting.

    I’m saying that comparmentalization is better than compromise. Either the two sources of truth both provide us with truths, or just keep the two separate until you see how they fit.

  3. The conflict between science and religion occurs only when each insists on straying out of its own domain and into that of its fellow.
    Religion that presumes to determine what scientific truth is based on religious texts cause conflict for its believers by presenting “facts” that cannot possibly be true. For example, lice spontaneously generating from sweat.
    Science that presumes to advance moral ideas based on hard, logical theories cause conflicts for its believers because, in order to present one concrete view, other equally legitimate views have to be surpressed. For example, the conclusion that global warming is man’s fault and we have to alter our behaviour to atone for it.

  4. micha says:


    I think you overstate it. There are areas of apparent conflict because the domains do overlap. Cosmogony, evolutionary biology, geology, etc… are all sciences. And the Torah does make claims about the same territory. Do we believe the archeologist’s theory that numbers the Canaanites of the days of Joshua and the Judges to be so few that 3mm immigrants would have overwhelmed them?

  5. Bob Miller says:

    1. One of my roommates at MIT proposed once in jest that once you get above the speed of light, Newtonian physics apply again.

    2. Lots of theories seem to work acceptably in practice, but, in principle, other theories might also seem to work acceptably in practice. For example, if Occam’s Razor is not taken to be an absolutely true guide, all kinds of options open up.

  6. Bob Miller says:

    There are modern theories showing how a tiny difference at one time can grow into a huge difference later. See, for example, http://en.wikipedia.org/wiki/Chaos_theory

    This is what makes weather prediction so dicey.

    What if the whole edifice of archeology is built up out of bricks with tiny flaws (resulting from bias in data gathering and interpretation) ? Would an outsider have the means to evaluate this edifice objectively, or is it essentially unverifiable?

  7. Bob Miller says:

    To clarify one of my items above:

    2. Lots of generally believed theories seem to work acceptably in practice, but, in principle, other, “unconventional” theories might also seem to work just as acceptably in practice. For example, if Occam’s Razor is not taken to be an absolutely true guide, all kinds of options open up.

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