Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Population Growth

Population Growth

Population size is dynamic, increasing with birth rates and immigration, and decreasing with death rates and emigration. In ideal conditions with unlimited resources, populations can increase exponentially, which plots as a J-shaped growth rate curve of population size against time. This type of curve is characteristic of newly-introduced invasive species, or populations that have suffered catastrophic declines and are rebounding.

The Number e as a Limit

The Number e as a Limit

The number e is a fundamental constant in calculus, playing a central role in describing continuous change, particularly exponential growth. It is most naturally defined through its relationship with the natural logarithm, which is the inverse of the exponential function with base e. This relationship allows e to be characterized using basic principles of differentiation rather than as an arbitrary numerical constant.A key property of the natural logarithm function, ln x, is that its derivative...

Numerical Calculations

Numerical Calculations

In engineering applications, the representation of the numerical value is critical. Presenting or reporting the answer is one of the essential parts of engineering practices. Numerical calculations are performed using handheld calculators or computers since numerically accurate answers are always preferred.
The solution to a problem is obtained using different methods. While manually solving algebraic symbols is one of the most common methods, the graphical method is often preferred. Computers...

Design Example: Capacitance Multiplier Circuit

Design Example: Capacitance Multiplier Circuit

In integrated circuit technology, a capacitance multiplier is often utilized to produce a larger capacitance value when a small physical capacitance falls short. This is achieved by a circuit that multiplies capacitance values by a factor of up to 1000, such that a 10-pF capacitor can replicate the performance of a 100-nF capacitor.
The circuit illustrated in Figure 1 below incorporates two op-amps, with the first operating as a voltage follower and the second acting as an inverting amplifier.

Exponential Equations for Modeling Growth

Exponential Equations for Modeling Growth

Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is...

Modeling with Differential Equations

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Exploring Amazonian Cognitive Diversity at Chana Research Station.

Topics in cognitive science·2026

Same author

The perception of quantity ain't number: Missing the primacy of symbolic reference.

The Behavioral and brain sciences·2021

Same author

Number - Biological Enculturation Beyond Natural Selection.

Trends in cognitive sciences·2017

Same author

Facing the sunrise: cultural worldview underlying intrinsic-based encoding of absolute frames of reference in aymara.

Cognitive science·2012

Same author

With the future behind them: convergent evidence from aymara language and gesture in the crosslinguistic comparison of spatial construals of time.

Cognitive science·2011

Same author

Gesture and metaphor comprehension: electrophysiological evidence of cross-modal coordination by audiovisual stimulation.

Brain and cognition·2009

Search research articles

Related Experiment Video

Updated: Mar 2, 2026

Daily Transfers, Archiving Populations, and Measuring Fitness in the Long-Term Evolution Experiment with Escherichia coli

Daily Transfers, Archiving Populations, and Measuring Fitness in the Long-Term Evolution Experiment with Escherichia coli

Published on: August 18, 2023

Is There Really an Evolved Capacity for Number?

Rafael E Núñez¹

¹Department of Cognitive Science, University of California, San Diego, La Jolla, CA 92093-0515, USA.

Trends in Cognitive Sciences

|May 21, 2017

Summary

Quantity discrimination abilities in humans and animals are not specific to number and arithmetic. True numerical cognition requires cultural input, distinguishing it from evolved quantical abilities.

Keywords:

culture evolution nativism number numerical cognition symbol

More Related Videos

A Comparative Approach for Quantitative Cell Counting Studies in Widely Different Mammalian Brains

A Comparative Approach for Quantitative Cell Counting Studies in Widely Different Mammalian Brains

Published on: January 16, 2026

Automated Microbial Cultivation and Adaptive Evolution using Microbial Microdroplet Culture System MMC

Automated Microbial Cultivation and Adaptive Evolution using Microbial Microdroplet Culture System MMC

Published on: February 18, 2022

Related Experiment Videos

Last Updated: Mar 2, 2026

Daily Transfers, Archiving Populations, and Measuring Fitness in the Long-Term Evolution Experiment with Escherichia coli

Daily Transfers, Archiving Populations, and Measuring Fitness in the Long-Term Evolution Experiment with Escherichia coli

Published on: August 18, 2023

A Comparative Approach for Quantitative Cell Counting Studies in Widely Different Mammalian Brains

A Comparative Approach for Quantitative Cell Counting Studies in Widely Different Mammalian Brains

Published on: January 16, 2026

Automated Microbial Cultivation and Adaptive Evolution using Microbial Microdroplet Culture System MMC

Automated Microbial Cultivation and Adaptive Evolution using Microbial Microdroplet Culture System MMC

Published on: February 18, 2022

Area of Science:

Cognitive Science
Evolutionary Biology
Comparative Psychology

Background:

A prevalent view posits that quantity discrimination is an evolved, number-specific capacity.
This perspective is challenged by teleological reasoning, flawed evolutionary concepts, and underemphasis on non-industrialized cultures and animal studies.

Purpose of the Study:

To critically re-evaluate the evolutionary origins of numerical cognition.
To propose a distinction between biologically evolved quantical cognition and culturally mediated numerical cognition.

Main Methods:

Critical analysis of existing literature on quantity discrimination.
Examination of evolutionary principles and cross-cultural data.
Reinterpretation of findings from animal cognition research.

Main Results:

The view of number-specific evolved abilities is based on flawed reasoning and selective evidence.
Quantical cognition (quantity discrimination) is biologically endowed but does not directly lead to numerical cognition.
Numerical cognition, including exact number and arithmetic, necessitates cultural mediation.

Conclusions:

A clear distinction between quantical and numerical cognition is essential.
Quantical abilities are precursors, not direct evolutionary products, of numerical cognition.
This framework impacts understanding the origins of other complex human capacities like language, music, and art.