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Monday, 7 July 2025

Humans Created in the Image and Likeness of God: Divine Potential and Personal Communion

 

Humans Created in the Image and Likeness of God: Divine Potential and Personal Communion




According to Orthodox Christian doctrine, rooted in the Holy Scriptures and the patristic tradition, man was created “in the image and according to the likeness of God (Genesis 1:26). This dual expression — κατεἰκόνα and καθὁμοίωσιν — has been the subject of profound theological reflection throughout the centuries.

The phrase “in the image” (κατεἰκόνα) refers to the ontological constitution of the human person. It affirms that man was fashioned by God with inherent dignity and endowed with rationality, freedom, creativity, and the capacity for love — attributes that reflect the very nature of God. This image is not physical but spiritual and existential, underscoring that every human being, irrespective of condition or circumstance, bears the indelible mark of divine origin.

The second part of the phrase, “according to the likeness” (καθὁμοίωσιν), indicates man’s potentiality — a calling rather than a static condition. While the image is granted from the moment of creation, the likeness is the goal towards which man must strive. It signifies the journey of deification (θέωσις), the process of becoming truly godlike, not by nature, but by grace. This ascent is realised through synergy: the cooperation between divine grace and human freedom. It is the path of repentance, virtue, prayer, and participation in the sacramental life of the Church.

Within this theological framework, the statement Man is not foreseen;he is communed invites a deeper, perhaps more mystical, consideration of personhood. At first glance, this phrase may appear to be in tension with the notion of divine foresight or providential design. However, a more careful reading reveals a profound truth consistent with Orthodox anthropology.

To say that man is “not foreseen” does not negate divine providence. God, in His omniscience, indeed foresees all things. He knows the full trajectory of each person’s life. But man, as a unique hypostasis — a person endowed with freedom and created for communion — cannot be reduced to a mere object of prediction or determinism. The phrase underscores that the human person is not merely the result of a blueprint or a divine schema that unfolds mechanically. Rather, he is a mystery to be experienced, encountered, loved — and ultimately, communed.

This communion is not merely a sentimental notion but a real participation in the life of God, most fully realised in the Eucharist and in the dynamic relationship between Creator and creature. In Orthodox theology, koinonia is not passive; it is transformative. God does not simply observe man’s ascent toward likeness; He invites and enables it through participation in His divine energies. Hence, while there is a divine intention — a telos — for each human being (i.e. theosis), the journey itself is one of freedom, love, and dynamic relationship, not fatalistic inevitability.

So then, are the phrases “Man was created in the image and likeness of God” and “Man is not foreseen; he is communed” compatible? Not only are they compatible — they are mutually enriching. The first establishes the theological foundation of man's nature and destiny; the second guards against reducing this destiny to a mechanical outcome. The likeness of God is not imposed; it is embraced. It is not a matter of prediction but of communion. God does not merely foresee who we will become; He desires to share His life with us in a communion of love that honours freedom.

In conclusion, the Orthodox understanding of the human person is one of profound dignity and hope. Man is made in God’s image — already bearing divine worth — and called to the likeness of God through cooperation with divine grace. He is not a product to be predicted, but a person to be loved and communed. In this lies both the mystery and the grandeur of human existence.

 

Thursday, 8 May 2025

Superanalysis

 

Superanalysis




Superanalysis in Mathematics and Science

Superanalysis is a modern mathematical framework that extends classical analysis into the realm of superspaces—geometric structures that incorporate both commuting (bosonic) and anticommuting (fermionic) variables. Rooted in the formalism of supersymmetry and supergeometry, the field was pioneered by Felix Berezin (Introduction to Superanalysis, 1987), with foundational contributions by DeWitt (1992), Kostant (1977), and Witten (1982).

Unlike classical analysis, which is confined to functions on real or complex domains, superanalysis operates on supermanifolds using supersmooth functions and Grassmann variables. This generalisation enables rigorous formulation of physical models involving fermions and bosons under a unified calculus, which is particularly potent in quantum field theory and string theory. Grassmann integration, central to this framework, plays a pivotal role in the Feynman path integral approach to quantum mechanics.

The advantages of superanalysis are multifold: it allows elegant representation of supersymmetric models, simplifies renormalisation, unifies algebraic and geometric constructs, and reveals symmetries hidden in conventional approaches. Its utility extends beyond physics to fields such as differential geometry, representation theory, condensed matter physics, random matrix theory, and even emerging applications in machine learning and cryptography (Efetov, 1997; Varadarajan, 2004).

Superanalysis in Life Decisions

Metaphorically, “superanalysis” refers to higher-order, multidimensional thinking—where decisions are made by integrating both rational (commutative) and emotional or ethical (anticommutative) factors. Psychologically, this aligns with metacognitive strategies described by Kahneman (Thinking, Fast and Slow, 2011) and sociologically reflects Luhmann’s (1995) theory of adaptive systems.

Although such deep analysis can lead to decision fatigue or “analysis paralysis”, it also promotes foresight, ethical awareness, and resilience. By embracing “superanalytical” thinking, individuals navigate complexity with greater clarity, leading to more conscientious and impactful life choices.

Thursday, 17 April 2025

The six “tribes” of quantum computers

 The six “tribes” of quantum computers



From the Bible we know the twelve tribes of Israel. In the era of quantum applications in which we live nowadays, it is worth knowing the six ‘tribes’ of quantum computers.

Quantum computers can be classified into six main ‘tribes’, each of which uses different technology and principles. Let's look at them one by one:

1.    Superconducting Qubits (Quantum Bits):

o  Description. The qubits are created using Josephson junctions (sandwiches of two superconductors enclosing a thin non-superconducting layer so that electrons can pass through the barrier - the coherence of the wavefunction in the superconductor results in a direct or alternating current), which allow for fast manipulation and measurement.

o   Key feature: It is currently one of the most developed and widely used types of quantum computers, used by companies such as IBM and Google.

2.    Trapped ions:

o    Description: This technology uses trapped ions as qubits, which are manipulated using lasers. Individual ions are held in place by electromagnetic fields and their quantum states are controlled by precise laser pulses.

  o      Key feature: They offer high coherence times and scalability, meaning they can maintain their quantum state for longer periods of time.

3.    Topological Qubits:

o   Description: this approach uses special states of matter, known as anyons, which are more resistant to errors due to their topological properties.

o   Key feature: Promises inherent fault tolerance, potentially making these qubits much more stable than others.

4.    Photonic quantum computers:

o    Description: These computers use photons as qubits. Quantum information is managed using optical devices such as beam splitters and phase shifters.

 o   Key feature: They can operate at room temperature and are excellent for certain types of quantum algorithms because of their speed and ease of integration into existing technologies.

5.    Quantum dots:

o     Description: Quantum dots are tiny semiconductor particles that can confine electrons or holes in three dimensions, acting as qubits. They rely on the spins of electrons or excitons to perform quantum operations.

o   Key feature: They can be integrated into existing semiconductor technology, potentially   leading to easier scalability.

6.    Neutral atoms:

o  Description: This type uses neutral atoms trapped in optical lattices or optical tweezers. The qubits are based on the internal states of these atoms and their interactions.

o  Key feature: They can provide significant flexibility in qubit design and are ideal for scalable quantum networks.


Each of these "tribes" offers a unique methodological approach to quantum computing, with different advantages and challenges, shaping the future of this technology.

Thursday, 10 April 2025

What Does “i” Do in Schrödinger’s Equation?

 

What Does “i” Do in Schrödinger’s Equation?



What Does “i” Do Here?

The imaginary unit 𝑖 is not just a mathematical trick — it plays a critical role:

✔ 1. It Encodes Oscillations (Wave Behavior)

  • Quantum particles are wave-like.
  • The evolution of waves over time is naturally described by complex exponentials:

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  • These oscillations are at the heart of interference, superposition, and tunneling in quantum mechanics.

➡ Without i, the wave-like time evolution wouldn’t be possible.


✔ 2. It Ensures Unitary Evolution

  • In quantum mechanics, probabilities must be conserved over time.
  • Time evolution via e−iHt/ℏ is unitary, meaning the total probability remains 1.
  • If “i” were missing, the equation would predict growing or shrinking probabilities (non-physical).


✔ 3. It Connects Time Evolution to Energy

  • “i” helps define how a quantum system changes with time:

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This complex exponential links energy (E) with how fast the wavefunction rotates in time.

  • The rotation is a phase change—and interference depends on these phases.


Analogy: Real-Life Example — Spinning Arrow

Think of the wave function as a spinning arrow (vector) on a clock face:

  • The length of the arrow represents probability amplitude.
  • The angle it makes (the phase) determines how it interferes with other arrows.
  • The rotation of this arrow over time is driven by i.

No “i” → no rotation → no phase change → no interference patterns → no quantum magic.


Table: Comparison of Equations With and Without “i”

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Graphical Representation: Oscillation vs. Exponential Decay

Let’s compare:

1. With “i”:

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Produces oscillating (cyclic) motion:

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2. Without “i”:

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Produces growth or decay – not suitable for describing quantum systems:

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Scientific Examples

▶ Electron in a Hydrogen Atom

  • The electron’s behavior is described by a wave function with a phase that evolves with time.
  • The interference of these phases gives rise to quantized energy levels.

▶ Quantum Tunneling

  • The wave function extends into a region where classical particles cannot go.
  • The complex phase (thanks to “i”) allows part of the wave to "leak through", explaining how tunneling occurs.


Summary in Simple Terms

  • The imaginary unit 𝑖 is not about imaginary things — it's essential to describing real quantum behavior.
  • It allows waves to evolve, probabilities to stay consistent, and interference to happen.
  • Without “i”, quantum mechanics would lose its core features and fail to describe the microscopic world.