On the geometry of four-dimensions and the relationship between metabolism and body mass

Blum, J. J.

doi:10.1016/0022-5193(77)90292-2

Cited by 74 publications

(43 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We then examine theoretical attempts to connect metabolic rate to mass. These include approaches based on dimensional analysis [1,18,31,32,33,34], four-dimensional biology [35,36], and nutrient-supply networks [22,37]. We find that none of these theories convincingly show that α = 3/4, rather than α = 2/3, should be expected.…”

Section: Introductionmentioning

confidence: 82%

Re-examination of the “3/4-law” of Metabolism

Dodds

Rothman

Weitz

2001

Journal of Theoretical Biology

522

490

View full text Add to dashboard Cite

Section: Introductionmentioning

confidence: 82%

Re-examination of the “3/4-law” of Metabolism

Dodds

Rothman

Weitz

2001

Journal of Theoretical Biology

522

490

View full text Add to dashboard Cite

“…If cells and organisms are non-Euclidian (as the scaling of the surface area and volume seems to indicate), they must exist in a higher dimensional state. Using analytical geometry, Blum 18 argued thus and adduced that the surface area for any n-dimensional object is proportional to its volume raised to the (n -1)/n power. Thus, for any Euclidean 3-dimensional object, S / V (n-1)/n / S / V (3-1)/3 / V 2/3 , whereas, for a 4-dimensional object, S / V (4 -1)/ 4 / V 3 /4 .…”

Section: The 3/4 Scaling Of Metabolic Ratesmentioning

confidence: 99%

Kleiber's Law: How theFire of Lifeignited debate, fueled theory, and neglected plants as model organisms

Niklas¹,

Kutschera

2015

Plant Signaling & Behavior

View full text Add to dashboard Cite

Size is a key feature of any organism since it influences the rate at which resources are consumed and thus affects metabolic rates. In the 1930s, size-dependent relationships were codified as "allometry" and it was shown that most of these could be quantified using the slopes of log-log plots of any 2 variables of interest. During the decades that followed, physiologists explored how animal respiration rates varied as a function of body size across taxa. The expectation was that rates would scale as the 2/3 power of body size as a reflection of the Euclidean relationship between surface area and volume. However, the work of Max Kleiber (1893Kleiber ( -1976 and others revealed that animal respiration rates apparently scale more closely as the 3/4 power of body size. This phenomenology, which is called "Kleiber's Law," has been described for a broad range of organisms, including some algae and plants. It has also been severely criticized on theoretical and empirical grounds. Here, we review the history of the analysis of metabolism, which originated with the works of Antoine L. Lavoisier (1743-1794) and Julius Sachs (1832-1897), and culminated in Kleiber's book The Fire of Life (1961; 2. ed. 1975). We then evaluate some of the criticisms that have been leveled against Kleiber's Law and some examples of the theories that have tried to explain it. We revive the speculation that intracellular exo-and endocytotic processes are resource delivery-systems, analogous to the supercellular systems in multicellular organisms. Finally, we present data that cast doubt on the existence of a single scaling relationship between growth and body size in plants.

show abstract

“…The suggestion that a fourth dimension of some sort is involved in explaining the 3/4 power is over 30 years old (Blum 1977). Hainsworth (1981), in his well-known book on physiology, briefly suggested that time may fill that role, and this picture clarified recently with the suggestion by Ginzburg and Damuth (2008) that generation time may well be the missing fourth dimension, to be added to the three spatial dimensions.…”

Section: Analogical Insights From Physicsmentioning

confidence: 99%

Analogical Thinking in Ecology: Looking beyond Disciplinary Boundaries

Colyvan

Ginzburg²

2010

The Quarterly Review of Biology

View full text Add to dashboard Cite

Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. The University of Chicago Press

show abstract

On the geometry of four-dimensions and the relationship between metabolism and body mass

Cited by 74 publications

References 2 publications

Re-examination of the “3/4-law” of Metabolism

Re-examination of the “3/4-law” of Metabolism

Kleiber's Law: How theFire of Lifeignited debate, fueled theory, and neglected plants as model organisms

Analogical Thinking in Ecology: Looking beyond Disciplinary Boundaries

Contact Info

Product

Resources

About