Pythagorean Harmonics in Multi-Millennial Solar Activity | Theodor Landscheidt

One of the first interdisciplinary approaches to a holistic understanding of our world was that of Pythagoras and his disciples. They created the theory of the fundamental significance of numbers in the objective world and in music. This theory reduced all existence to number, meaning that all entities are ultimately reducible to numerical relationships that link not only mathematics to music but also to acoustics, geometry, and astronomy. Even the dependence of the dynamics of world structure on the interaction of pairs of opposites—of which the even–odd polarity essential to numbers is primary—emerges from these numerical relationships. Pythagoras would have been pleased to learn of attractors opposing in character, created by simple feedback loops of numbers, and forming tenuous boundaries—dynamic sites of instability and creativity.

Pythagoras exploring harmony and ratio with various musical

instruments; Franchinus Gaffurius, Theorica musicae, 1492.

Pythagorean thinking deeply influenced the development of classical Greek philosophy and medieval European thought, especially the astrological belief that the planetary harmony of the universe affects everything, including terrestrial affairs, through space–time configurations of cosmic bodies. People were intrigued by the precision of numerical relationships between musical harmonies, which deeply touch the human soul, and the prosaic arithmetical ratios of integers. This connection was first demonstrated by Pythagoras himself in the sixth century B.C. In his famous experiment, a stretched string on a monochord was divided by simple arithmetical ratios—1:2, 2:3, 3:4, 4:5, and 5:6—and plucked. It was a Eureka moment when he discovered that these respective partitions of the string create the consonant intervals of harmony.

 

One tone is not yet music. One might say it is only a promise of music. The promise is fulfilled, and music comes into being, only when one tone follows another. Strictly speaking, therefore, the basic elements of music are not individual tones but the movements between tones. Each of these movements spans a certain pitch distance. The pitch distance between two tones is called an interval. It is the basic element of melody and of individual musical motion. Melody is a succession of intervals rather than of tones. Intervals can be consonant or dissonant.

 

[ Nodes of a vibrating string are harmonics. Conversely, antinodes

—points of maximum amplitude—occur midway between nodes. ]

 

It was Pythagoras’ great discovery to see that the ratios of the first small integers up to six give rise to consonant intervals; the smaller these integers, the more complete the resonance. A string divided in the ratio 1:2 yields the octave (C–C), an equisonance of the fundamental tone. The ratio 2:3 yields the fifth (C–G); 3:4 the fourth (C–F); 4:5 the major third (C–E); and 5:6 the minor third. These correspond to the consonant intervals of octave, fifth, fourth, major third, minor third, and the sixth. The pairs of notes given in brackets are examples of the respective consonances.

 

The minor sixth, created by the ratio 5:8, seems to go beyond the limit of six. Yet eight—the only integer greater than six involved here—is the third power of two and thus a member of the series of consonant numbers. Eight is created by an octave operation, which produces absolutely equisonant tones. All authorities agree that, besides the equisonant octave, there are no consonant intervals other than the third, the fourth, the fifth, and the sixth. If more than two notes are to be consonant, each pair of them must also be consonant.

 

As mentioned already, the most complete consonance within the range of an octave is the major perfect chord C–E–G (4:5:6), which unites the major third and the fifth with the fundamental note. These concepts of harmony and consonant intervals are formed by the first terms in the series of overtones, or harmonics, produced by a vibrating string. [...] Whenever there is a musical sound, there is an addition of harmonics that relate the fundamental tone to an infinity of overtones, which influence the quality of the consonant fundamental. The overtones up to the sixth harmonic represent the consonant intervals: the octave, the fifth, the fourth, the major third, the minor third, and the sixth.

Figure 19: Smoothed time series of consecutive impulses of the torque (IOT), with epochs indicated by dots. The resulting wave pattern corresponds to the secular cycle of sunspot activity. The average wavelength is 166 years, with each extremum occurring at mean intervals of 83 years, aligned with a maximum in the secular sunspot cycle. These maxima, as identified by Wolfgang Gleissberg, are marked by bold arrows. Minima occur when the wave approaches zero. This wave pattern reflects the influence of solar system configurations that generate impulses of the torque.

Figure 34 shows the combination of the consonant intervals known as the major sixth (3:5) and the minor sixth (5:8) as they emerge in solar-system processes over thousands of years. These intervals are marked by vertical triangles and large numbers. The curve depicts the supersecular variation of energy in the secular torque wave, part of which was shown in points along the curve represent epochs of extrema, labeled by Aₛ numbers from −64 to +28, corresponding to the period from 5259 BC to AD 2347. The mean cycle length is 391 years. Black triangles indicate maxima in the corresponding supersecular sunspot cycle, while open triangles indicate minima. When the energy exceeds certain quantitative thresholds, shown by hatched horizontal lines, a phase jump occurs in the correlated supersecular sunspot cycle. These critical phases are marked by vertical dotted lines. A new phase jump is expected around 2030.

It points toward a supersecular minimum comparable to the Egyptian minimum (E) around 1369 BC, a prolonged period marked by notable cooling and glacier advance. The ratio 3:5:8, representing the major and minor sixth, marks the intervals that separate these rare phase jumps indicated by the vertical dotted lines. The 317.7-year period of the triple conjunction of Jupiter, Saturn, and Uranus is also involved in this relationship, as shown by the small numbers beneath the large numbers at the top of the figure.

[...] Another confirmation of the hypothesis that consonant intervals play an important role with respect to the Sun's eruptional activity are the connections presented in Figure 34 that cover thousands of years. It has been shown in Figure 19 that consecutive impulses of the torque (IOT) in the Sun’s motion about the center of mass (CM) of the solar system, when taken to constitute a smoothed time series, form a wave-pattern the positive and negative extrema (±As​) of which coincide with maxima in the secular sunspot cycle. This Gleissberg cycle, with a mean period of 83 years, which modulates the intensity of the 11-year sunspot cycle, is in turn modulated by a supersecular sunspot cycle with a mean period of about 400 years. The Maunder Minimum of sunspot activity in the 17th century and a supersecular maximum in the 12th century are features of this supersecular cycle. It seems to be related to the energy in the secular wave presented in Figure 19.

This energy may be measured by squared values of the secular extrema ±As​. When these values are taken to form another smoothed time series, a supersecular wave emerges as plotted in Figure 34. It runs parallel with the supersecular sunspot cycle. Its mean period is 391 years, but it varies from 166 to 665 years. Each dot in the plot indicates the epoch of a secular extremum (±As​). These epochs are numbered from -64 to +28 and range from 5259 B.C. to 2347 A.D. Black triangles indicate maxima in the correlated supersecular sunspot curve and white triangles minima. The medieval maximum, which was together a climate optimum (O), the Spoerer Minimum (S), and the Maunder Minimum (M) are marked by respective abbreviations. The extrema in the supersecular wave properly reflect all marked peaks and troughs in the supersecular sunspot curve derived from radiocarbon data.
 

Quoted from:
Theodor Landscheidt (1989) - Sun-Earth-Man: A Mesh of Cosmic Oscillations.

 

Angular Momentum and Past/Future Solar Activity, 1600-2200: JUP-NEP resonance of 22.13y mirrors Sun’s 22y magnetic cycle. JUP-NEP squares to solar equator align with 11y solar minima; sub-harmonics like JUP-URA-NEP at 11.09y track sunspot fluctuations. Centuries of data show minimal drift (0.6 ±1.5y), suggesting planetary periods act as solar activity pacemakers. 

 

Geoff J. Sharp (2013) - Are Uranus and Neptune Responsible for Solar Grand Minima and Solar Cycle Modulation? 
Nicola Scafetta (2012) - Multi-scale harmonic model for solar and climate cyclical variation throughout the Holocene based on Jupiter-Saturn tidal frequencies plus the 11-year solar dynamo cycle.

 

See also:

Theodor Landscheidt (1990) - Cosmic Regulation of Cycles in Nature and Economy. 

Theodor Landscheidt (1989) - Mini-Crash in Tune with Cosmic Rhythms. 

Theodor Landscheidt (1989) - Predictable Cycles in Geomagnetic Activity and Ozone Levels.

Joachim-Ernst Berendt (1987) - The "Law of the Octave": The World Is Sound.

Aleksander Valkov (2025) - Helioeconomics: Solar Cycles as the Hidden Pacemaker of Global Economic Fluctuations. 

Alexander L. Chizhevsky (2025) - Mass Excitability during Solar Cycle 25 (2019–2030). 

Vladimir A. Belkin (2014) - "Cosmic Cycles of Global Conjuncture" and Outlook into 2035. 

TPR (2015) - The Same, The Other, and The Essence: Plato's Theology of Arithmetic. 

TPR - S&P 500 Index vs Jupiter – Saturn Cycle, 2017-2020. 

 TPR - Solar Activity and Financial Markets.

Mass Excitability during Solar Cycle 25 (2019–2030) | Alexander L. Chizhevsky

Solar Cycle 25, which spans from December 2019 to approximately late 2030, exemplifies Alexander L. Chizhevsky's (1897–1964) historiometric  framework. This model, laid out in his 1924 article "The Physical Factors of the Historical Process," links human psychological "excitability" to solar activity over the average 11-year solar cycle: 

"In each century, the universal cycle of historical events is repeated exactly 9 times. Throughout the world history of Mankind, beginning with 500 B.C. and until the present time, in each century I have discovered 9 clearly outlined concentrations of the initial moments of historical events. Thus, it can be considered that each cycle of the general historical, military or social activity of humanity is equal, on average, to 11 years." 

 

 Чижевский Александр Леонидович (1924) - Физические факторы исторического процессa.

 

  NOAA's latest Solar Cycle 25 Sunspot Number Progression Update, December 12, 2025.

 

 

"Figure 1: Percentage ratio of occurrences of historical events to years and periods

of the [11-year solar] cycle. Average output for 500 years (15th –20th centuries)."

Through analysis of over 2,000 major historical events from 500 BCE to 1922 CE across numerous countries, he determined that approximately 80% of significant upheavals—such as wars, revolutions, riots, migrations, and social unrest—occurred during periods of elevated solar activity, particularly the ascending phase and maximum of the sunspot cycle. In contrast, solar minima were associated with relative societal calm and passivity. According to Chizhevsky, each solar cycle divides into four phases: 

 

(I) Minimum Excitability (~3 years, 5% of "historical events" per Figure 1), 

(II) Growth Excitability (~2.5 years, 20% of events), 

(III) Maximum Excitability (~3 years, 60% of events), and 

(IV) Decline Excitability (~2.5 years, 15% of events). 

 

These are harmonized with NOAA's phases of the solar cycle (Minimum ~3 years, Rising ~4 years, Maximum ~3 years, Declining ~7 years) to fit the observed progression, with the smoothed peak at 160.9 sunspot numbers in October 2024. As of December 2025, the cycle is in the "Maximum Excitability" phase amid sustained high activity.

Phase I: Minimum Excitability (December 2019-November 2022): This phase aligns with NOAA's Solar Minimum in December 2019, featuring minimal sunspots and stable magnetic poles, comprising ~5% of "historical events" per Chizhevsky's Figure 1 (see above). It represents societal disunity and cultural focus:

 

"The characteristic features of this period are the following: disunity of human masses, indifference of the human masses to political and military issues, peace-loving mood of the human masses, compliance, tolerance, etc. The appearance of these psychological signs in the historically active human masses in the 1st period of the cycle is usually accompanied by the absence of any desire for any struggle for an idea or right, and therefore entails easy capitulation, surrender, throwing down of arms, flight from the battlefield, etc. 

 

» Absence of any desire for any struggle. «

[...] In the memoirs of contemporaries and in historical studies, this period is noted for its general peace-loving mood, unwillingness to enter into any disputes, the end of most military actions and the triumph of the principle of non-intervention in international and national military-political life. 

 

[...] Here the spiritual activity of Man begins, cultural values are created, pure art and science are placed in the corner of social life, replacing the stormy turmoil of recent days and devaluing with their achievements everything created hastily and precariously. In the period of minimum, humanity strives for calm, rests from the worries of previous years and gathers physical strength for the inevitably approaching new era of [social] unrest."

Phase II: Increasing Excitability (December 2022 – mid-2025): Corresponding to NOAA's Growth/Rising Phase, with escalating sunspots and initial pole shifts, this phase spans ~20% of "historical events" per Figure 1. It signals emerging ideologies and unity:

"Already the beginning of this period in historical studies is characterized by a significantly greater rise in the excitement of human masses than in the preceding period. There is still no unity of the masses of people; only little by little do the parties and groups that had fallen apart during the period of minimal excitability begin to reorganize, leaders are outlined, programs are defined. The power of suggestion manifests itself among the human masses: statesmen, military leaders, orators, the press are regaining their importance. 

 

» Impatience and nervousness of the masses. «

 

Questions, political and military, begin to appear from behind the horizon of public life and gradually become more acute. The tendency to perseverate homogeneous thoughts is noticeable everywhere, filling the mental activity of the human masses. In spite of the will of individuals, the concentration on the same military or political themes, in the presence of, of course, favorable factors, gradually increases; ideas circulating among the human masses begin to dominate. 

 

[...] At the end of the 2nd period, which can gradually assume a stormy character and reveal the impatience and nervousness of the masses of people, we notice one of the most important phenomena of the military-political life of communities, namely: the desire to unite the various nationalities that make up a given community for the purpose of defense or attack, and the merging of various political groups to counter other political groups. 

 

The significance of this period is that it lays the foundation for the further development of historical events during a given cycle in a given human community and, in part, even predetermines their course during the period of maximum excitability."

In October 2023 NOAA’s Space Weather Prediction Center released a revised prediction for solar activity during Solar

Cycle 25, and concluded that solar activity will increase more quickly and peak at a higher level than previously predicted.

  

Phase III: Maximum Excitability in Solar Cycle 25 (mid-2025 – mid-2028): As of December 2025, Solar Cycle 25 is firmly entrenched in Phase III, the period of Maximum Excitability, which spans mid-2025 to mid-2028. Encompassing NOAA's Solar Maximum, with peak sunspots, flares, and ejections, this phase accounts for ~60% of "historical events" per Figure 1. It drives transformative mass actions. This phase, as delineated by Chizhevsky, represents the apex of solar activity's influence on human behavior, characterized by heightened psychological tension and collective mobilization:

"This is the main stage of development of each cycle, resolving the world-historical problems of humanity and founding new historical epochs. It incites humanity to the greatest follies and the greatest benefactions: it embodies ideas in life by means of the shedding of blood and the clanking of iron. 

 

 » The entire vast area of human madness. «

 

[...] Never does the influence of leaders, military leaders, orators, the press, etc., reach such a tremendous force as during the period of maximum intensity of the sunspot-forming activity of the Sun. During this period, sometimes one well-timed word or one gesture is enough to move entire armies and the masses. 

 

[...] The period of maximum excitability may just be called the period of the emergence of the face of human masses and the sounding of the voice of the people. [...] The masses of people thirst for movement, the troops are restrained with difficulty, the soldiers are inclined to mutiny, and the people — to anarchy. In a word, the excitement increases unusually and the human organism seems to demand a discharge.

 

» The shedding of blood and the clanking of iron. « 

 

[...] The basis of the above is the unanimity of the masses of people, which is especially clearly outlined in this period when resolving any military or political issues. [...] This brings with it various phenomena characteristic of any struggle, and mass movements of people usually undergo abnormal deviations. Sometimes the height of the struggle reveals the entire vast area of human madness, instability and passion. 

 

[...] Thus, the ground is prepared for the solution of questions of a world-historical nature — the ground on which systems of human communities are erected."

 

Chizhevsky describes Phase III as "the main stage of development of each cycle, resolving the world-historical problems of humanity and founding new historical epochs. It incites humanity to the greatest follies and the greatest benefactions: it embodies ideas in life by means of the shedding of blood and the clanking of iron." 

 

He emphasizes that during Phase III, "the mass activity of humanity all over the surface of the Earth, given the presence in human societies of economical, political or military exciting factors, reaches the maximum tension, manifesting itself in psycomotoric pandemics: revolutions, insurrections, expeditions, migrations etc., creating new formations in the existence of separate states and new historical epochs in the life of humanity."
 

» Solution of questions of a world-historical nature. «

Plasma Tornado Erupts on the Sun. 

Russian Academy of Sciences Footage, December 11-12, 2025.

 

Central to Phase III is the amplification of leadership influence and mass unanimity. Chizhevsky notes, "Never does the influence of leaders, military leaders, orators, the press, etc., reach such a tremendous force as during the period of maximum intensity of the sunspot-forming activity of the Sun. During this period, sometimes one well-timed word or one gesture is enough to move entire armies and the masses." 

 

Πόλεμος πάντων μὲν πατήρ ἐστι, πάντων δὲ βασιλεύς, καὶ τοὺς μὲν θεοὺς 

ἔδειξε τοὺς δὲ ἀνθρώπους, τοὺς μὲν δούλους ἐποίησε τοὺς δὲ ἐλευθέρους.

» War is both father and king of all; some he has shown forth as gods 

and others as men, some he has made slaves and others free. «
Heraclitus, also known as "The Dark One" (ὁ Σκοτεινός); 

Fragment DK22B53, ca. 500 BCE.

This fosters "the unanimity of the masses of people, which is especially clearly outlined in this period when resolving any military or political issues," leading to rapid dissemination of movements: "the astonishing speed of the spread of popular uprisings and mass [social] movements in general." However, this surge can devolve into extremes, as "mass movements of people usually undergo abnormal deviations. Sometimes the height of the struggle reveals the entire vast area of human madness, instability and passion. Elemental violence, bitterness, frenzy, thirst for revenge, epidemics of murder, panic, pogroms, devastating raids, desperate battles, mass exterminations, bloodbaths, as well as uprisings, mutinies, coupled with the manifestation of fanaticism and heroism — reach their apogee."

 

Major revolutions align with Solar Maximums, e.g.: 1775–1783 American War of Independence (Cycle 2), 1789 French Revolution (Cycle 3), 1910 Mexican Revolution (Cycle 14), 1906 and 1917 Russian Revolutions (Cycles 14–15), 1959 Cuban Revolution (Cycle 19), 1979 Revolution in Iran and Nicaragua (Cycle 21), Soviet collapse in 1989–91 (Cycle 22), 1998-2001 Revolution in Venezuela (Cycle 23), Arab Spring 2011 (Cycle 24), 2024 MIGA-MAGA Revolution (Cycle 25).

Contemporary events in 2025, amid elevated sunspot activity, resonate with these dynamics. Geopolitically, persistent conflicts such as the NATO-Russia war in Ukraine, the wars in and around Palestine and Sudan exhibit intensified diplomatic pressures for ceasefires, reflecting Chizhevsky's notion of resolving "world-historical problems." The fall of Assad's regime in Syria has spurred migrations and regional realignments, akin to the "migrations etc., creating new formations in the existence of separate states." Escalations in nuclear proliferation, space security, and hybrid warfare underscore the phase's potential for "devastating raids" and "mass exterminations." 

 

Phase IV: Decreasing excitability (mid-2028 – December 2030): This phase matches NOAA's Declining/Falling Phase, with waning sunspots and field preparation for reversal, representing ~15% of events per Figure 1. It fosters resolution and fatigue:

"The period of decline in excitability is, as it were, an echo of the stormy period of struggle and unrest that preceded it, the highest degree of tension of which has already passed, and a general need for calm and peace is felt. If there is a war, its heat gradually dies down, sluggishness is observed in military actions, their tempo slows down. 

 

» The depressive state of the masses. «

 

[...] Leaders, commanders, orators lose those forces that in the preceding period fettered the masses and forced them to obedience. The masses are already subject to suggestion with difficulty. [...] This lack of unanimity in the 4th period of the historiometric cycle can be called a stumbling block on which any newly-begun uprising, any mass activity risks being wrecked, since concentrated action, due to the reduction and relaxation of the connecting forces, becomes impossible. 

 

[...] Finally, the general decline in excitability is replaced by a psycho-physical state that can be called enervation. Popular assemblies and representations are dispersed without protest, uprisings are easily suppressed, wars do not flare up, and also peace negotiations are mechanically caused by the depressive state of the masses of people, which is often facilitated by physical exhaustion and fatigue."

 

Regarding the economic and financial realm during the remainder of Solar Cycle 25 into around 2030, Helioeconomist Aleksander Valkov recently put forth the following forecast: Given that Solar Cycle 25 reached a stronger-than-expected maximum around 2024–2025, his HELI index indicates that the current global economic expansion has already peaked or is in its final stage. The model forecasts an accelerating contraction phase leading into a major multicycle trough centered on the early 2030s—precisely the period when the next solar minimum is expected. Leonty Miroshnichenko's findings support Valkov's correlation:  "On average, the difference between the peaks and troughs of solar activity and economic cycles does not exceed six months." Furthermore, historical analysis shows that 88% of recessions since the 1800s and 100% of major financial crises occurred during the downturn of sunspot cycles.

 

 Reference:

 Alexander L. Chizhevsky (1924) - The Physical Factors of the Historical Process.

(Чижевский Александр Леонидович (1924) - Физические факторы исторического процессa.)

Aleksander Valkov (2025) - Helioeconomics: Solar Cycles as the Hidden Pacemaker of Global Economic Fluctuations. 

Leonty Miroshnichenko (2023) - Kondratiev Waves Aligned with Solar Cycles.  

Suitbert Ertel (1996) - Space Weather and Revolutions - Chizhevsky's Heliobiological Claim Scrutinized.  

Gustave Le Bon (1913) - The Psychology of Revolution. 

Kemalhan Gerçeker et al. (November 26, 2025) - Simplex Projection Predictions of the Remainder of Solar Cycle 25. 

 NOAA (2025) - Solar Cycle Sunspot Number Progression.

"Cosmic Cycles of Global Conjuncture" & Outlook into 2035 | Vladimir A. Belkin

Vladimir Belkin's 2014 study "Cosmic Cycles of Global Conjuncture" (КОСМИЧЕСКИЕ ЦИКЛЫ МИРОВОЙ КОНЪЮНКТУРЫ) synthesized the interconnections between solar activity cycles and global economic fluctuations. Belkin posited a robust inverse relationship between peaks in solar activity—measured via Wolf sunspot numbers—and subsequent declines in world output and US GDP growth, drawing on the fields of Heliobiology and Helioeconomics. Employing correlation and lagged regression analyses over extended historical periods, he demonstrated cyclical alignments with Juglar (7–11 years) and Kitchin (3–5 years) business cycles to forecast economic deterioration in 2014–2015.

Chart 1 above ("Kitchin and Juglar cycles of world output as a function of solar activity, 1961–2013.") illustrates Kitchin and Juglar cycles in world output (1961–2013) against lagged solar activity. Dual axes show Wolf numbers (left, solid line) peaking inversely to output growth (right, dashed line, one-year lag), with visual mirroring and R² ≈ 0.99 in segments, confirming short-term solar-driven volatility.

Extending this, chart 2 ("Kitchin and Juglar cycles in US GDP as a function of solar activity, 1798–2013.") applies the same to US GDP (1798–2013), demonstrating remarkable persistence over two centuries. The inverse pattern—solar peaks followed by GDP troughs—spans industrial revolutions and institutional changes, with a correlation of –0.88, underscoring the robustness of heliobiological influences on economic history.

Chart 3 ("Strong inverse relationship between cycles of world output and cycles of solar activity.") depicts the strong inverse between normalized world output cycles and solar activity (1961–2013 extended), with Wolf numbers (solid) and lagged growth index (dashed) as near-mirror images. A correlation of –0.87 highlights how solar rises precipitate growth falls, validating Belkin's claim of solar activity as a primary cycle determinant.

Focusing on extrema, chart 4 ("Strong inverse relationship between monthly extremes in Wolf numbers and annual world-output growth with a one-year lag.") presents a scatter plot of monthly Wolf peaks (x-axis) against annual world growth one year later (y-axis, 1964–2009), with a downward-sloping regression (R² = 0.7597). Higher solar maxima predict deeper slowdowns, offering a precise metric for crisis intensity.

Chart 5 ("Strong inverse relationship between the long cycle of world output and the long cycle of monthly solar-activity maxima.") addresses long cycles, plotting world output growth around solar maxima years (1968–2000, black line) against average Wolf numbers. A stepwise decline in growth per successive maximum (correlation –0.85) reveals secular trends, where weakening solar cycles since 1968 coincide with diminishing global expansions.

Complementing the above charts, Table 1 quantifies post-maxima declines: for solar peaks in 1968, 1979, 1989, and 2000, world growth fell by –2.90%, –2.01%, –2.42%, and –2.19% within two years, respectively. Belkin projected –2.38% for 2013 (delayed Cycle 24), forecasting a 2014–2015 downturn to ~2.0% growth, aligning with emerging-market vulnerabilities.

Collectively, this substantiates high statistical significance, with lags explaining physiological delays (e.g., geomagnetic storms reducing blood flow by 32–40%, fostering pessimism). Methodologically, Belkin employed:

• Lagged correlation analysis: Economic growth is regressed against solar activity with a one-year lag, reflecting delayed physiological impacts (e.g., solar maxima precede growth troughs). 
• Cycle decomposition: Juglar and Kitchin cycles are isolated via smoothing and differencing, then overlaid on solar series to visualize inversions.
• Regression modeling: Scatter plots with fitted lines quantify relationships, reporting R² and correlation coefficients (e.g., –0.87 to –0.88 overall).
• Forecasting via extrapolation: Historical patterns inform projections, adjusted for NASA solar forecasts (e.g., delayed Cycle 24 peak in 2013–2014).

Applying Belkin’s methodology to current solar forecasts yields the following calibrated projections for 2025–2035:

• 2025–2026: Cycle 25’s prolonged maximum (SSN peak 160.8 in Oct 2024, extending to mid-2025) signals imminent slowdown via the lagged inverse correlation (r ≈ –0.87; chart 3); expect global GDP deceleration of 2.0–2.5% from 2024 levels to 1.5–2.0%, mirroring Table 1’s –2.38% post-peak drop, with initial geomagnetic volatility worsening emerging-market risks (as in Belkin’s 2013–2014 forecast).
• 2027–2030: Cycle 25 minimum (2029–2030) reverses the trend, producing upswings similar to post-minimum recoveries (charts 1 and 2); secular weakening (chart 5) moderates amplitude, but growth should accelerate to 3.5–4.5% by 2029, driven by solar quiescence and reduced crisis propensity.
• 2031–2035: Cycle 26 onset (2029–2032 start, moderate SSN max ~131–160 ca. 2040–2043) brings rising solar activity that erodes gains per the inverse linkage (chart 4, R² = 0.76), yielding 1–2% cumulative drag by 2035 and possible mild recession if the cycle exceeds forecasts; overall 2025–2035 average growth 2.5–3.0% (chart 5 declining envelope), contingent on astrophysical accuracy.

Solar-timing uncertainties (e.g., exact Cycle 26 start) require integration with endogenous models, and post-2025 validation will refine accuracy.

Reference:
Vladimir A. Belkin (2014) - Cosmic Cycles of Global Conjuncture (КОСМИЧЕСКИЕ ЦИКЛЫ МИРОВОЙ КОНЪЮНКТУРЫ).

Vladimir A. Belkin holds a Doctorate in Economic Sciences and is a leading research scientist at the Chelyabinsk Institute of Economics, Ural Branch of the Russian Academy of Sciences, and Professor of Economics, Finance, and Accounting at the Chelyabinsk Branch of the Russian Presidential Academy of National Economy and Public Administration. Renowned for pioneering helioeconomics, his extensive publications—over 90 since 2008—explore inverse correlations between solar activity cycles and global economic fluctuations, with recent works (up to 2025) analyzing GDP growth and commodity prices.

See also:

Vladimir A. Belkin (2024)  - Economic Crises and Solar Activity Extrema: Calculation of the Fall in the World GDP Growth in 2025. 

Vladimir A. Belkin (2024) - Strong Inverse Correlation between Ap Index and Gold Price. 

Vladimir A. Belkin (2024) - 2025-2027 Oil Price Decline Linked to Solar Cycle Activity.   

Aleksander Valkov (2025) - Helioeconomics: Solar Cycles as the Hidden Pacemaker of Global Economic Fluctuations.

Leonty Miroshnichenko (2023) - Kondratiev Waves Aligned with Solar Cycles.  

Tatiana Alexandrovna Zenchenko & Tamara Konstantinovna Breus (2021) - The Possible Effect of Space Weather Factors on Various Physiological Systems of the Human Organism.

A 2020 first-light video from the Daniel K. Inouye Solar Telescope captures solar granulation at unprecedented 30 km resolution in 705 nm light, revealing convection cells approximately the size of Texas, where hot plasma rises in bright centers and sinks along dark intergranular lanes, driving surface heat transfer while tiny magnetic bright points channel energy to the million-degree corona. Amid Solar Cycle 25's heightened activity—having peaked in late 2024 with elevated sunspot numbers exceeding initial forecasts—such high-resolution observations continue to refine models of solar flares and space weather impacts.